Trainable-parameter-free structural-diversity message passing for graph neural networks.

Graph Neural Networks (GNNs) have achieved strong performance in structured data modeling such as node classification. However, real-world graphs often exhibit heterogeneous neighborhoods and complex feature distributions, while mainstream approaches rely on many learnable parameters and apply uniform aggregation to all neighbors. This lack of explicit modeling for structural diversity often leads to representation homogenization, semantic degradation, and poor adaptability under challenging conditions such as low supervision or class imbalance. To address these limitations, we propose a trainable-parameter-free graph neural network framework, termed the Structural-Diversity Graph Neural Network (SDGNN), which operationalizes structural diversity in message passing. At its core, the Structural-Diversity Message Passing (SDMP) mechanism performs within-group statistics followed by cross-group selection, thereby capturing neighborhood heterogeneity while stabilizing feature semantics. SDGNN further incorporates complementary structure-driven and feature-driven partitioning strategies, together with a normalized-propagation-based global structural enhancer, to enhance adaptability across diverse graphs. Extensive experiments on nine public benchmark datasets and an interdisciplinary PubMed citation network demonstrate that SDGNN consistently outperforms mainstream GNNs, especially under low supervision, class imbalance, and cross-domain transfer. The full implementation, including code and configurations, is publicly available at: https://github.com/mingyue15694/SGDNN/tree/main.