While a growing body of literature has been studying new Graph Neural Networks (GNNs) that work on both homophilic and heterophilic graphs, little has been done on adapting classical GNNs to less-homophilic graphs. Although the ability to handle less-homophilic graphs is restricted, classical GNNs still stand out in several nice properties such as efficiency, simplicity, and explainability. In this work, we propose a novel graph restructuring method that can be integrated into any type of GNNs, including classical GNNs, to leverage the benefits of existing GNNs while alleviating their limitations. Our contribution is threefold: a) learning the weight of pseudo-eigenvectors for an adaptive spectral clustering that aligns well with known node labels, b) proposing a new density-aware homophilic metric that is robust to label imbalance, and c) reconstructing the adjacency matrix based on the result of adaptive spectral clustering to maximize the homophilic scores. The experimental results show that our graph restructuring method can significantly boost the performance of six classical GNNs by an average of 25% on less-homophilic graphs. The boosted performance is comparable to state-of-the-art methods.

翻译：尽管已有大量文献研究适用于同质性和异质性图的新型图神经网络（GNNs），但针对如何使经典GNNs适应低同质性图的研究却很少。虽然经典GNNs处理低同质性图的能力有限，但其在效率、简洁性和可解释性等方面仍具有显著优势。本文提出一种新颖的图重构方法，该方法可集成至包括经典GNNs在内的任意类型GNNs中，在保留现有GNNs优势的同时缓解其局限性。我们的贡献体现在三个方面：a) 学习伪特征向量的权重以实现与已知节点标签良好对齐的自适应谱聚类；b) 提出一种对标签不均衡具有鲁棒性的新型密度感知同质性度量；c) 基于自适应谱聚类结果重构邻接矩阵以最大化同质性分数。实验结果表明，我们的图重构方法在低同质性图上能够将六种经典GNNs的性能平均提升25%，提升后的性能可与最新方法相媲美。