Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data. Existing methods, such as GAEs, have demonstrated effectiveness but typically rely on message-passing mechanisms that assume homophily, leading to performance degradation on heterophilous graphs, where connected nodes exhibit dissimilar features. This homophily bias results in the loss of critical high-frequency components that are essential for identifying heterophilous patterns. To address these challenges, we propose \textsc{AlignGAE}, a novel extension of \textit{MaskGAE} that preserves the full frequency spectrum through complementary view alignment. Our framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes. We further propose theoretically grounded NID alignment strategies that ensure semantic consistency across views while preserving their distinct characteristics. Through comprehensive spectral analysis, we demonstrate that \textsc{AlignGAE} achieves optimal representation properties when the alignment loss converges. Extensive experiments across 12 benchmark datasets validate our approach, showing that \textsc{AlignGAE} outperforms state-of-the-art methods by up to 18.7\% on heterophilous graphs in node classification, while maintaining competitive performance on homophilous graphs. Our results establish a new paradigm for frequency-aware graph representation learning.
Node classification in graph neural networks (GNNs) has been widely applied in various fields of graph analysis. GNNs achieve high-accuracy node classification in homophilous graphs, where nodes with the same class label tend to be connected. However, their performance remains limited in heterophilous graphs, where nodes with different class labels are more likely to be connected. In particular, current GNNs derived from graph convolutional networks cannot capture higher-order class label connectivity, which is frequently observed in real-world heterophilous graphs. To address this issue, we propose a novel classifier, Label Context Classifier (LCC), designed to capture higher-order class label connectivity in directed graphs. LCC estimates the class label of a target node by leveraging label context embeddings that are generated through four distinct types of walks. In addition, our approach allows the integration of LCC and any GNN by adaptively learning their importance. Experimental results demonstrate that GNNs integrated with LCC outperform SOTA methods and the label context embeddings improve the node classification performance in heterophilous directed graphs.