# On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs

arXiv: https://arxiv.org/abs/2107.01495 · HTML: https://mlsanity.com/paper/2107.01495/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 68 references that are in the map.
- First posted on arXiv 3 Jul 2021.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Random Features Strengthen Graph Neural Networks](https://mlsanity.com/paper/2002.03155/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Rethinking pooling in graph neural networks](https://mlsanity.com/paper/2010.11418/) (2020)
- [Graph Policy Network for Transferable Active Learning on Graphs](https://mlsanity.com/paper/2006.13463/) (2020)
- [Graph Convolutional Networks for Graphs Containing Missing Features](https://mlsanity.com/paper/2007.04583/) (2020)
- [Learning on Attribute-Missing Graphs](https://mlsanity.com/paper/2011.01623/) (2020)
- [Path Integral Based Convolution and Pooling for Graph Neural Networks](https://mlsanity.com/paper/2006.16811/) (2020)
- [Graph Cross Networks with Vertex Infomax Pooling](https://mlsanity.com/paper/2010.01804/) (2020)
- [Optimization of Graph Neural Networks with Natural Gradient Descent](https://mlsanity.com/paper/2008.09624/) (2020)
- [On Node Features for Graph Neural Networks](https://mlsanity.com/paper/1911.08795/) (2019)
- [A simple yet effective baseline for non-attributed graph classification](https://mlsanity.com/paper/1811.03508/) (2018)
- [Understanding Regularized Spectral Clustering via Graph Conductance](https://mlsanity.com/paper/1806.01468/) (2018)
- [Contextual Graph Markov Model: A Deep and Generative Approach to Graph Processing](https://mlsanity.com/paper/1805.10636/) (2018)

## Built on by (most cited first, 30 of 49)

- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation](https://mlsanity.com/paper/2212.01842/) (2022)
- [NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics](https://mlsanity.com/paper/2306.06202/) (2023)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [Data-Efficient Brain Connectome Analysis via Multi-Task Meta-Learning](https://mlsanity.com/paper/2206.04486/) (2022)
- [BrainNNExplainer: An Interpretable Graph Neural Network Framework for Brain Network based Disease Analysis](https://mlsanity.com/paper/2107.05097/) (2021)
- [Accurate Node Feature Estimation with Structured Variational Graph Autoencoder](https://mlsanity.com/paper/2206.04516/) (2022)
- [TouchUp-G: Improving Feature Representation through Graph-Centric Finetuning](https://mlsanity.com/paper/2309.13885/) (2023)
- [PTGB: Pre-Train Graph Neural Networks for Brain Network Analysis](https://mlsanity.com/paper/2305.14376/) (2023)
- [Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors](https://mlsanity.com/paper/2604.19028/) (2026)
- [Graph Neural Network-based Android Malware Classification with Jumping Knowledge](https://mlsanity.com/paper/2201.07537/) (2022)
- [Feature Distribution on Graph Topology Mediates the Effect of Graph Convolution: Homophily Perspective](https://mlsanity.com/paper/2402.04621/) (2024)
- [Graph Neural Networks for Graph Drawing](https://mlsanity.com/paper/2109.10061/) (2021)
- [How Can Graph Neural Networks Help Document Retrieval: A Case Study on CORD19 with Concept Map Generation](https://mlsanity.com/paper/2201.04672/) (2022)
- [Recovering Missing Node Features with Local Structure-based Embeddings](https://mlsanity.com/paper/2309.09068/) (2023)
- [Out of Sight, Still in Mind: Reasoning and Planning about Unobserved Objects with Video Tracking Enabled Memory Models](https://mlsanity.com/paper/2309.15278/) (2023)
- [GRAIN: Exact Graph Reconstruction from Gradients](https://mlsanity.com/paper/2503.01838/) (2025)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [Rethinking the Effectiveness of Graph Classification Datasets in Benchmarks for Assessing GNNs](https://mlsanity.com/paper/2407.04999/) (2024)
- [Enhancing GNNs Performance on Combinatorial Optimization by Recurrent Feature Update](https://mlsanity.com/paper/2407.16468/) (2024)
- [IOHunter: Graph Foundation Model to Uncover Online Information Operations](https://mlsanity.com/paper/2412.14663/) (2024)
- [Deep Fraud Detection on Non-attributed Graph](https://mlsanity.com/paper/2110.01171/) (2021)
- [Decoupled Subgraph Federated Learning](https://mlsanity.com/paper/2402.19163/) (2024)
- [Link Prediction with Untrained Message Passing Layers](https://mlsanity.com/paper/2406.16687/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [GRAN is superior to GraphRNN: node orderings, kernel- and graph embeddings-based metrics for graph generators](https://mlsanity.com/paper/2307.06709/) (2023)

## Abstract (arXiv)

Graph neural networks (GNNs) have been widely used in various graph-related problems such as node classification and graph classification, where superior performance is mainly established when natural node features are available. However, it is not well understood how GNNs work without natural node features, especially regarding the various ways to construct artificial ones. In this paper, we point out the two types of artificial node features, i.e., positional and structural node features, and provide insights on why each of them is more appropriate for certain tasks, i.e., positional node classification, structural node classification, and graph classification. Extensive experimental results on 10 benchmark datasets validate our insights, thus leading to a practical guideline on the choices between different artificial node features for GNNs on non-attributed graphs. The code is available at https://github.com/zjzijielu/gnn-positional-structural-node-features.