GraphSB: Boosting Imbalanced Node Classification on Graphs through Structural Balance

Imbalanced node classification is a critical challenge in graph learning, where most existing methods typically utilize Graph Neural Networks (GNNs) to learn node representations. These methods can be broadly categorized into the data-level and the algorithm-level. The former aims to synthesize minority-class nodes to mitigate quantity imbalance, while the latter tries to optimize the learning process to highlight minority classes. However, neither of them addresses the inherently imbalanced graph structure, which is a fundamental factor that incurs majority-class dominance and minority-class assimilation in GNNs. Our theoretical analysis further supports this critical insight. Therefore, we propose GraphSB (Graph Structural Balance), a novel framework that incorporates Structural Balance as a key strategy to address the underlying imbalanced graph structure before node synthesis. Structural Balance performs a two-stage structure optimization: Structure Enhancement that mines hard samples near decision boundaries through dual-view analysis and enhances connectivity for minority classes through adaptive augmentation, and Relation Diffusion that propagates the enhanced minority context while simultaneously capturing higher-order structural dependencies. Thus, GraphSB balances structural distribution before node synthesis, enabling more effective learning in GNNs. Extensive experiments demonstrate that GraphSB significantly outperforms the state-of-the-art methods. More importantly, the proposed Structural Balance can be seamlessly integrated into state-of-the-art methods as a simple plug-and-play module, increasing their accuracy by an average of 4.57%.

💡 Research Summary

GraphSB addresses the pervasive problem of class‑imbalanced node classification in graph neural networks (GNNs) by targeting the often‑overlooked structural imbalance of the graph itself. Existing solutions fall into two categories: data‑level methods that synthesize additional minority‑class nodes, and algorithm‑level methods that modify loss functions or regularization to emphasize minority classes. While these approaches mitigate the quantity imbalance, they ignore the fact that minority‑class nodes typically have sparser neighborhoods, leading to biased neighbor aggregation, information dilution, and gradient dominance by majority‑class nodes. The authors provide a rigorous theoretical analysis showing three detrimental mechanisms: (1) Information Dilution – the degree disparity τ between majority and minority nodes amplifies the over‑squashing effect, causing rapid decay of minority information along multi‑hop paths; (2) Gradient Dominance – the imbalance ratio β makes gradients from majority nodes dominate parameter updates, suppressing learning signals from minority nodes; (3) Minority‑Class Assimilation – as GNN depth increases, the centroid distance between classes decays exponentially, effectively collapsing minority representations into the majority subspace.

To counteract these mechanisms, GraphSB introduces a two‑stage Structural Balance framework.
Stage 1 – Structure Enhancement first mines “hard samples” that lie near decision boundaries using a dual‑view strategy. In the feature view, a lightweight MLP predicts class probabilities; nodes whose top‑1 prediction is a majority class while the top‑2 prediction is a minority class (with a second‑highest probability above a threshold ξ) are flagged. In the neighbor view, soft‑voting over normalized adjacency aggregates neighbor predictions, and only nodes whose neighborhood consensus favors the minority class are retained. This dual‑view filtering isolates nodes that suffer from minority‑subspace compression yet are surrounded by minority‑supporting neighborhoods. For each selected hard sample, adaptive augmentation connects it to the most similar minority‑class anchor in the training set, but only if the similarity exceeds the anchor’s average neighbor similarity τ_v, thereby preserving homophily while enriching minority connectivity.

Stage 2 – Relation Diffusion propagates the newly added edges through multi‑step diffusion. At each diffusion step k, the node embeddings are updated via learnable functions ϕ_k and ψ_k, weighted by a diffusion coefficient λ_k. The process captures higher‑order structural dependencies and ensures that the enriched minority context spreads throughout the graph without overwhelming the original topology. The final embedding Z^{(k)} is a weighted sum of all diffusion steps, seamlessly integrating with any downstream GNN.

GraphSB is deliberately modular: after structural balancing, any existing data‑level synthesis method (e.g., GraphMixup) can be applied unchanged. The authors demonstrate that the structural‑balance module can be plugged into state‑of‑the‑art pipelines, yielding an average accuracy boost of 4.57 % across eight benchmark datasets (Cora, Citeseer, Pubmed, ogbn‑arxiv, etc.). Detailed experiments show consistent improvements in overall accuracy, macro‑F1, and especially minority‑class F1 scores. Ablation studies confirm that both stages contribute: structure enhancement alone already separates minority embeddings in t‑SNE visualizations, while relation diffusion mitigates performance degradation in deep GNNs (10+ layers) by counteracting over‑squashing.

Complexity analysis in the appendix indicates that the additional computation scales linearly with the number of hard samples and added edges, adding negligible overhead to typical GNN training pipelines.

In summary, GraphSB provides a theoretically grounded, practically effective solution to structural imbalance in graphs. By first rebalancing the graph topology—identifying and reinforcing minority‑class connections—and then diffusing this enriched context, the framework improves representation quality for minority nodes and lifts the performance ceiling of existing imbalance‑handling techniques. Its plug‑and‑play nature makes it readily adoptable in real‑world graph learning systems, marking a significant step toward fair and accurate node classification on imbalanced networks.