# Node-wise Diffusion for Scalable Graph Learning

arXiv: https://arxiv.org/abs/2305.14000 · HTML: https://mlsanity.com/paper/2305.14000/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2023.

## Built on by (most cited first, 17 of 17)

- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [Contrastive Graph Representation Learning with Adversarial Cross-view Reconstruction and Information Bottleneck](https://mlsanity.com/paper/2408.00295/) (2024)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)
- [Learning to Approximate Adaptive Kernel Convolution on Graphs](https://mlsanity.com/paper/2401.11840/) (2024)
- [Efficient Topology-aware Data Augmentation for High-Degree Graph Neural Networks](https://mlsanity.com/paper/2406.05482/) (2024)
- [Leveraging Large Language Models for Effective Label-free Node Classification in Text-Attributed Graphs](https://mlsanity.com/paper/2412.11983/) (2024)
- [Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach](https://mlsanity.com/paper/2403.07954/) (2024)
- [Effective Edge-wise Representation Learning in Edge-Attributed Bipartite Graphs](https://mlsanity.com/paper/2406.13369/) (2024)
- [GegenNet: Spectral Convolutional Neural Networks for Link Sign Prediction in Signed Bipartite Graphs](https://mlsanity.com/paper/2508.19907/) (2025)
- [Unifews: You Need Fewer Operations for Efficient Graph Neural Networks](https://mlsanity.com/paper/2403.13268/) (2024)
- [ScaDyG:A New Paradigm for Large-scale Dynamic Graph Learning](https://mlsanity.com/paper/2501.16002/) (2025)
- [Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening](https://mlsanity.com/paper/2505.14033/) (2025)
- [Mixture of Scope Experts at Test: Generalizing Deeper Graph Neural Networks with Shallow Variants](https://mlsanity.com/paper/2409.06998/) (2024)
- [Acceleration Algorithms in GNNs: A Survey](https://mlsanity.com/paper/2405.04114/) (2024)
- [Focus Where It Matters: Graph Selective State Focused Attention Networks](https://mlsanity.com/paper/2410.15849/) (2024)
- [Rethinking Semi-Supervised Node Classification with Self-Supervised Graph Clustering](https://mlsanity.com/paper/2511.19976/) (2025)
- [Rethinking Message Passing Neural Networks with Diffusion Distance-guided Stress Majorization](https://mlsanity.com/paper/2511.19984/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown superior performance for semi-supervised learning of numerous web applications, such as classification on web services and pages, analysis of online social networks, and recommendation in e-commerce. The state of the art derives representations for all nodes in graphs following the same diffusion (message passing) model without discriminating their uniqueness. However, (i) labeled nodes involved in model training usually account for a small portion of graphs in the semisupervised setting, and (ii) different nodes locate at different graph local contexts and it inevitably degrades the representation qualities if treating them undistinguishedly in diffusion. To address the above issues, we develop NDM, a universal node-wise diffusion model, to capture the unique characteristics of each node in diffusion, by which NDM is able to yield high-quality node representations. In what follows, we customize NDM for semisupervised learning and design the NIGCN model. In particular, NIGCN advances the efficiency significantly since it (i) produces representations for labeled nodes only and (ii) adopts well-designed neighbor sampling techniques tailored for node representation generation. Extensive experimental results on various types of web datasets, including citation, social and co-purchasing graphs, not only verify the state-of-the-art effectiveness of NIGCN but also strongly support the remarkable scalability of NIGCN. In particular, NIGCN completes representation generation and training within 10 seconds on the dataset with hundreds of millions of nodes and billions of edges, up to orders of magnitude speedups over the baselines, while achieving the highest F1-scores on classification.