ICEPool: Enhancing Graph Pooling Networks with Inter-cluster Connectivity

TL;DR

ICEPool tackles the gap in hierarchical graph pooling by explicitly modeling inter-cluster connectivity. It combines Connection Entropy-augmented Graph Attention and SVDPool to capture both the distribution and directionality of inter-cluster edges, enabling reconstruction of the inter-cluster adjacency and preserving global graph structure. The approach is theoretically grounded, with a reconstruction proposition for inter-cluster connectivity, and empirically validated across multiple datasets and backbones, showing reliable performance gains. While introducing extra computation, ICEPool provides a flexible and broadly compatible enhancement for graph-level tasks in diverse pooling-based GNN architectures.

Abstract

Hierarchical Pooling Models have demonstrated strong performance in classifying graph-structured data. While numerous innovative methods have been proposed to design cluster assignments and coarsening strategies, the relationships between clusters are often overlooked. In this paper, we introduce Inter-cluster Connectivity Enhancement Pooling (ICEPool), a novel hierarchical pooling framework designed to enhance model's understanding of inter-cluster connectivity and ability of preserving the structural integrity in the original graph. ICEPool is compatible with a wide range of pooling-based GNN models. The deployment of ICEPool as an enhancement to existing models effectively combines the strengths of the original model with ICEPool's capability to emphasize the integration of inter-cluster connectivity, resulting in a more comprehensive and robust graph-level representation. Moreover, we make theoretical analysis to ICEPool's ability of graph reconstruction to demonstrate its effectiveness in learning inter-cluster relationship that is overlooked by conventional models. Finally, the experimental results show the compatibility of ICEPool with wide varieties of models and its potential to boost the performance of existing graph neural network architectures.

Figures (4)

• Figure 1: General workflow of traditional graph pooling networks.
• Figure 2: Illustration of Connection Entropy$\mathcal{H}$. Both graphs have the same number of inter-cluster edges between cluster $i$ and cluster $j$, resulting in identical coarsened edge weights $A_{coar}[i, j] = 5$. However, the connection patterns differ: in the left example, edges are evenly distributed across nodes, while in the right, they are concentrated on a few nodes. The coarsened representation $A_{coar}$ fails to capture this distinction due to its symmetry and reliance on edge count alone. In contrast, $\mathcal{H}[i, j]$ reflects the distribution of connections, making it a more expressive measure of inter-cluster structure.
• Figure 3: Illustration of SVDPool. Node features are modulated by aggregation weights during message passing.
• Figure 4: ICEPool architecture. A SVDPool layer is added parallel to standard graph pooling layer, while the standard GNN layers that follows is replaced by a Connection Entropy-enhenced GAT layer.