# Parameter-Free Structural-Diversity Message Passing for Graph Neural Networks

arXiv: https://arxiv.org/abs/2508.19884 · HTML: https://mlsanity.com/paper/2508.19884/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Agent-based Graph Neural Networks](https://mlsanity.com/paper/2206.11010/) (2022)
- [Structural Diversity and Homophily: A Study Across More than One Hundred Big Networks](https://mlsanity.com/paper/1602.07048/) (2016)
- [Characterizing the structural diversity of complex networks across domains](https://mlsanity.com/paper/1710.11304/) (2017)
- [A Community Detection and Graph Neural Network Based Link Prediction Approach for Scientific Literature](https://mlsanity.com/paper/2401.02542/) (2024)
- [RSEA-MVGNN: Multi-View Graph Neural Network with Reliable Structural Enhancement and Aggregation](https://mlsanity.com/paper/2408.07331/) (2024)
- [An Experimental Study of Structural Diversity in Social Networks](https://mlsanity.com/paper/1909.03543/) (2019)
- [Truss-based Structural Diversity Search in Large Graphs](https://mlsanity.com/paper/2007.05437/) (2020)
- [Harnessing Collective Structure Knowledge in Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2405.10633/) (2024)
- [TANGNN: a Concise, Scalable and Effective Graph Neural Networks with Top-m Attention Mechanism for Graph Representation Learning](https://mlsanity.com/paper/2411.15458/) (2024)
- [Citation Structural Diversity: A Novel and Concise Metric Combining Structure and Semantics for Literature Evaluation](https://mlsanity.com/paper/2501.02429/) (2025)
- [The Strength of Structural Diversity in Online Social Networks](https://mlsanity.com/paper/1906.00756/) (2019)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown remarkable performance in structured data modeling tasks such as node classification. However, mainstream approaches generally rely on a large number of trainable parameters and fixed aggregation rules, making it difficult to adapt to graph data with strong structural heterogeneity and complex feature distributions. This often leads to over-smoothing of node representations and semantic degradation. To address these issues, this paper proposes a parameter-free graph neural network framework based on structural diversity, namely SDGNN (Structural-Diversity Graph Neural Network). The framework is inspired by structural diversity theory and designs a unified structural-diversity message passing mechanism that simultaneously captures the heterogeneity of neighborhood structures and the stability of feature semantics, without introducing additional trainable parameters. Unlike traditional parameterized methods, SDGNN does not rely on complex model training, but instead leverages complementary modeling from both structure-driven and feature-driven perspectives, thereby effectively improving adaptability across datasets and scenarios. Experimental results show that on eight public benchmark datasets and an interdisciplinary PubMed citation network, SDGNN consistently outperforms mainstream GNNs under challenging conditions such as low supervision, class imbalance, and cross-domain transfer. This work provides a new theoretical perspective and general approach for the design of parameter-free graph neural networks, and further validates the importance of structural diversity as a core signal in graph representation learning. To facilitate reproducibility and further research, the full implementation of SDGNN has been released at: https://github.com/mingyue15694/SGDNN/tree/main