Eigenvector Distance-Modulated Graph Neural Network: Spectral Weighting for Enhanced Node Classification

Graph Neural Networks (GNNs) face significant challenges in node classification across diverse graph structures. Traditional message passing mechanisms often fail to adaptively weight node relationships, thereby limiting performance in both homophilic and heterophilic graph settings. We propose the Eigenvector Distance-Modulated Graph Neural Network (EDM-GNN), which enhances message passing by incorporating spectral information from the graph’s eigenvectors. Our method introduces a novel weighting scheme that modulates information flow based on a combined similarity measure that balances feature-based similarity with structural similarity derived from eigenvector distances. This approach creates a more discriminative aggregation process that adapts to the underlying graph topology without requiring prior knowledge of homophily characteristics. We implement a hierarchical neighborhood aggregation framework that utilizes these spectral weights across multiple powers of the adjacency matrix. Experimental results on benchmark datasets demonstrate that EDM-GNN achieves competitive performance with state-of-the-art methods across both homophilic and heterophilic settings. Our approach provides a unified solution for node classification problems with strong theoretical foundations in spectral graph theory and significant empirical improvements in classification accuracy.