Energy Levels Based Graph Neural Networks for Heterophily

The representation power of graph neural networks (GNNs) under heterophily has drawn much attention recently, in which some connected nodes do not have common labels or similar features. Previous approaches typically incorporate high-order neighbourhoods’ information so as to reinforce aggregation operation. However, they do not directly face with heterophily in first-order neighbours. To deal with this problem, we propose the energy levels guided GNNs in which energy levels of classes are incorporated for better expressiveness. We prove that the label with higher energy level would imply higher energy in the spectrum of the normalized graph Laplacian. Experiments on common benchmark datasets show the effectiveness of the proposed approach.