Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering

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: [label= *)] learning the weight of pseudo-eigenvectors for an adaptive spectral clustering that aligns well with known node labels, proposing a new density-aware homophilic metric that is robust to label imbalance, and reconstructing the adjacency matrix based on the result of adaptive spectral clustering to maximize 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\