GNNs Getting ComFy: Community and Feature Similarity Guided Rewiring

TL;DR

This paper introduces three novel graph rewiring strategies, including a hybrid approach, to improve GNN performance by enhancing community structure and feature similarity, supported by theoretical analysis and extensive experiments.

Contribution

It proposes new rewiring methods that explicitly target community and feature similarity, offering computational efficiency and improved GNN generalization.

Findings

ComFy outperforms spectral gap optimization in experiments.

Community-aware rewiring improves label-community alignment.

Feature similarity rewiring increases global homophily.

Abstract

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.