# Position-aware Graph Neural Networks

arXiv: https://arxiv.org/abs/1906.04817 · HTML: https://mlsanity.com/paper/1906.04817/

## Key facts

- Cited by 203 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2019.

## Built on by (most cited first, 30 of 203)

- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Graph Inductive Biases in Transformers without Message Passing](https://mlsanity.com/paper/2305.17589/) (2023)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [ROLAND: Graph Learning Framework for Dynamic Graphs](https://mlsanity.com/paper/2208.07239/) (2022)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Federated Graph Classification over Non-IID Graphs](https://mlsanity.com/paper/2106.13423/) (2021)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Parameter Prediction for Unseen Deep Architectures](https://mlsanity.com/paper/2110.13100/) (2021)
- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification](https://mlsanity.com/paper/2406.08993/) (2024)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Neo-GNNs: Neighborhood Overlap-aware Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2206.04216/) (2022)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modeling](https://mlsanity.com/paper/2106.05223/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Reconstruction for Powerful Graph Representations](https://mlsanity.com/paper/2110.00577/) (2021)
- [A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests](https://mlsanity.com/paper/2302.07090/) (2023)
- [Language-Agnostic Representation Learning of Source Code from Structure and Context](https://mlsanity.com/paper/2103.11318/) (2021)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Topology-Imbalance Learning for Semi-Supervised Node Classification](https://mlsanity.com/paper/2110.04099/) (2021)
- [Neighborhood-aware Scalable Temporal Network Representation Learning](https://mlsanity.com/paper/2209.01084/) (2022)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)
- [Knowledge-aware Coupled Graph Neural Network for Social Recommendation](https://mlsanity.com/paper/2110.03987/) (2021)

## Abstract (arXiv)

Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the position/location of a given node with respect to all other nodes of the graph. Here we propose Position-aware Graph Neural Networks (P-GNNs), a new class of GNNs for computing position-aware node embeddings. P-GNN first samples sets of anchor nodes, computes the distance of a given target node to each anchor-set,and then learns a non-linear distance-weighted aggregation scheme over the anchor-sets. This way P-GNNs can capture positions/locations of nodes with respect to the anchor nodes. P-GNNs have several advantages: they are inductive, scalable,and can incorporate node feature information. We apply P-GNNs to multiple prediction tasks including link prediction and community detection. We show that P-GNNs consistently outperform state of the art GNNs, with up to 66% improvement in terms of the ROC AUC score.