# Geodesic Graph Neural Network for Efficient Graph Representation Learning

arXiv: https://arxiv.org/abs/2210.02636 · HTML: https://mlsanity.com/paper/2210.02636/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 66 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 30 of 42)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [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)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)

## Built on by (most cited first, 19 of 19)

- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [GOFA: A Generative One-For-All Model for Joint Graph Language Modeling](https://mlsanity.com/paper/2407.09709/) (2024)
- [A Theory of Link Prediction via Relational Weisfeiler-Leman on Knowledge Graphs](https://mlsanity.com/paper/2302.02209/) (2023)
- [Path Neural Networks: Expressive and Accurate Graph Neural Networks](https://mlsanity.com/paper/2306.05955/) (2023)
- [Revisiting Link Prediction: A Data Perspective](https://mlsanity.com/paper/2310.00793/) (2023)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Extending the Design Space of Graph Neural Networks by Rethinking Folklore Weisfeiler-Lehman](https://mlsanity.com/paper/2306.03266/) (2023)
- [Investigating Out-of-Distribution Generalization of GNNs: An Architecture Perspective](https://mlsanity.com/paper/2402.08228/) (2024)
- [MAG-GNN: Reinforcement Learning Boosted Graph Neural Network](https://mlsanity.com/paper/2310.19142/) (2023)
- [TAGLAS: An atlas of text-attributed graph datasets in the era of large graph and language models](https://mlsanity.com/paper/2406.14683/) (2024)
- [SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning](https://mlsanity.com/paper/2303.03379/) (2023)
- [Efficient Link Prediction via GNN Layers Induced by Negative Sampling](https://mlsanity.com/paper/2310.09516/) (2023)
- [Learning Scalable Structural Representations for Link Prediction with Bloom Signatures](https://mlsanity.com/paper/2312.16784/) (2023)
- [Understanding Generalization in Node and Link Prediction](https://mlsanity.com/paper/2507.00927/) (2025)
- [T- Hop: A framework for studying the importance path information in molecular graphs for chemical property prediction](https://mlsanity.com/paper/2407.14270/) (2024)
- [HoGA: Higher-Order Graph Attention via Diversity-Aware k-Hop Sampling](https://mlsanity.com/paper/2411.12052/) (2024)
- [Chordless Structure: A Pathway to Simple and Expressive GNNs](https://mlsanity.com/paper/2505.19188/) (2025)
- [Global to Local: Topology-Preserving Adaptive Graph Pooling via Granular-Ball](https://mlsanity.com/paper/2609.04978/) (2026)
- [Multi-granularity Adaptive Hypergraph Representation Learning via Granular-ball](https://mlsanity.com/paper/2609.05574/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have recently been applied to graph learning tasks and achieved state-of-the-art (SOTA) results. However, many competitive methods run GNNs multiple times with subgraph extraction and customized labeling to capture information that is hard for normal GNNs to learn. Such operations are time-consuming and do not scale to large graphs. In this paper, we propose an efficient GNN framework called Geodesic GNN (GDGNN) that requires only one GNN run and injects conditional relationships between nodes into the model without labeling. This strategy effectively reduces the runtime of subgraph methods. Specifically, we view the shortest paths between two nodes as the spatial graph context of the neighborhood around them. The GNN embeddings of nodes on the shortest paths are used to generate geodesic representations. Conditioned on the geodesic representations, GDGNN can generate node, link, and graph representations that carry much richer structural information than plain GNNs. We theoretically prove that GDGNN is more powerful than plain GNNs. We present experimental results to show that GDGNN achieves highly competitive performance with SOTA GNN models on various graph learning tasks while taking significantly less time.