H³GNNs: Harmonizing Heterophily and Homophily in GNNs via Joint Structural Node Encoding and Self-Supervised Learning

2025/04/16 by Rui Xue, Xue, Rui, Tianfu Wu +1
Computer Science · #Advanced Graph Neural Networks #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Multimodal Machine Learning Applications #Social and Information Networks (cs.SI)

paper · pdf · doi:10.48550/arxiv.2504.11699

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Graph Neural Networks (GNNs) struggle to balance heterophily and homophily in representation learning, a challenge further amplified in self-supervised settings. We propose H³GNNs, an end-to-end self-supervised learning framework that harmonizes both structural properties through two key innovations: (i) Joint Structural Node Encoding. We embed nodes into a unified space combining linear and non-linear feature projections with K-hop structural representations via a Weighted Graph Convolution Network(WGCN). A cross-attention mechanism enhances awareness and adaptability to heterophily and homophily. (ii) Self-Supervised Learning Using Teacher-Student Predictive Architectures with Node-Difficulty Driven Dynamic Masking Strategies. We use a teacher-student model, the student sees the masked input graph and predicts node features inferred by the teacher that sees the full input graph in the joint encoding space. To enhance learning difficulty, we introduce two novel node-predictive-difficulty-based masking strategies. Experiments on seven benchmarks (four heterophily datasets and three homophily datasets) confirm the effectiveness and efficiency of H³GNNs across diverse graph types. Our H³GNNs achieves overall state-of-the-art performance on the four heterophily datasets, while retaining on-par performance to previous state-of-the-art methods on the three homophily datasets.

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Related

• Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs
• Self-Attention Empowered Graph Convolutional Network for Structure Learning and Node Embedding
• The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs
• Adapting to Heterophilic Graph Data with Structure-Guided Neighbor Discovery
• Is Homophily a Necessity for Graph Neural Networks?