GNNs Getting ComFy: Community and Feature Similarity Guided Rewiring
This work addresses performance bottlenecks in GNNs for graph-based learning tasks, offering incremental improvements through targeted rewiring strategies.
The paper tackles the problem of improving graph neural network (GNN) performance by analyzing how graph rewiring affects generalization, showing that minimizing the spectral gap can enhance it when community structure aligns with node labels, and proposes three rewiring strategies (ComMa, FeaSt, ComFy) that achieve competitive results in experiments.
Maximizing the spectral gap through graph rewiring has been proposed to enhance the performance of message-passing graph neural networks (GNNs) by addressing over-squashing. However, as we show, minimizing the spectral gap can also improve generalization. To explain this, we analyze how rewiring can benefit GNNs within the context of stochastic block models. Since spectral gap optimization primarily influences community strength, it improves performance when the community structure aligns with node labels. Building on this insight, we propose three distinct rewiring strategies that explicitly target community structure, node labels, and their alignment: (a) community structure-based rewiring (ComMa), a more computationally efficient alternative to spectral gap optimization that achieves similar goals; (b) feature similarity-based rewiring (FeaSt), which focuses on maximizing global homophily; and (c) a hybrid approach (ComFy), which enhances local feature similarity while preserving community structure to optimize label-community alignment. Extensive experiments confirm the effectiveness of these strategies and support our theoretical insights.