# Co-embedding of Nodes and Edges with Graph Neural Networks

arXiv: https://arxiv.org/abs/2010.13242 · HTML: https://mlsanity.com/paper/2010.13242/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

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

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- [Learning to Count Isomorphisms with Graph Neural Networks](https://mlsanity.com/paper/2302.03266/) (2023)
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- [An Adaptive Graph Pre-training Framework for Localized Collaborative Filtering](https://mlsanity.com/paper/2112.07191/) (2021)
- [Deep graphical regression for jointly moderate and extreme Australian wildfires](https://mlsanity.com/paper/2308.14547/) (2023)
- [Non-backtracking Graph Neural Networks](https://mlsanity.com/paper/2310.07430/) (2023)
- [Automated Graph Learning via Population Based Self-Tuning GCN](https://mlsanity.com/paper/2107.04713/) (2021)
- ["The Pedestrian next to the Lamppost" Adaptive Object Graphs for Better Instantaneous Mapping](https://mlsanity.com/paper/2204.02944/) (2022)
- [Graph Learning and Its Advancements on Large Language Models: A Holistic Survey](https://mlsanity.com/paper/2212.08966/) (2022)
- [Self-Supervised Graph Representation Learning via Topology Transformations](https://mlsanity.com/paper/2105.11689/) (2021)
- [TWIG: Towards pre-hoc Hyperparameter Optimisation and Cross-Graph Generalisation via Simulated KGE Models](https://mlsanity.com/paper/2402.06097/) (2024)
- [A Network Science perspective of Graph Convolutional Networks: A survey](https://mlsanity.com/paper/2301.04824/) (2023)
- [GRANDE: a neural model over directed multigraphs with application to anti-money laundering](https://mlsanity.com/paper/2302.02101/) (2023)
- [KG-Augmented Executable CoT for Mathematical Coding](https://mlsanity.com/paper/2508.04072/) (2025)
- [Low-Latency Relay Selection in NR-V2X Vehicular Communications via Graph Isomorphism Networks with Edge Features](https://mlsanity.com/paper/2607.14176/) (2026)
- [PoseGraphNet++: Enriching 3D Human Pose with Orientation Estimation](https://mlsanity.com/paper/2308.11440/) (2023)
- [Veni, Vidi, Vici: Solving the Myriad of Challenges before Knowledge Graph Learning](https://mlsanity.com/paper/2402.06098/) (2024)
- [Graph Edge Representation via Tensor Product Graph Convolutional Representation](https://mlsanity.com/paper/2406.14846/) (2024)
- [Multistage non-deterministic classification using secondary concept graphs and graph convolutional networks for high-level feature extraction](https://mlsanity.com/paper/2411.06212/) (2024)
- [Graph Neural Networks Based Analog Circuit Link Prediction](https://mlsanity.com/paper/2504.10240/) (2025)
- [Edge-boosted graph learning for functional brain connectivity analysis](https://mlsanity.com/paper/2504.14796/) (2025)
- [GNN-Enabled Robust Hybrid Beamforming with Score-Based CSI Generation and Denoising](https://mlsanity.com/paper/2511.06663/) (2025)
- [Improving Graph Embeddings in Machine Learning Using Knowledge Completion with Validation in a Case Study on COVID-19 Spread](https://mlsanity.com/paper/2511.12071/) (2025)
- [Bi-View Embedding Fusion: A Hybrid Learning Approach for Knowledge Graph's Nodes Classification Addressing Problems with Limited Data](https://mlsanity.com/paper/2511.13044/) (2025)
- [Spectral and Spatial Graph Learning for Multispectral Solar Image Compression](https://mlsanity.com/paper/2512.24463/) (2025)
- [On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman](https://mlsanity.com/paper/2609.16412/) (2026)
- [AI-Driven Real-Time Relay Optimisation in Smart Urban NR-V2X Networks via Learning-to-Optimise Graph Neural Networks](https://mlsanity.com/paper/2609.20271/) (2026)

## Abstract (arXiv)

Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large number of machine learning tasks. Graph embedding is a way to transform and encode the data structure in high dimensional and non-Euclidean feature space to a low dimensional and structural space, which is easily exploited by other machine learning algorithms. We have witnessed a huge surge of such embedding methods, from statistical approaches to recent deep learning methods such as the graph convolutional networks (GCN). Deep learning approaches usually outperform the traditional methods in most graph learning benchmarks by building an end-to-end learning framework to optimize the loss function directly. However, most of the existing GCN methods can only perform convolution operations with node features, while ignoring the handy information in edge features, such as relations in knowledge graphs. To address this problem, we present CensNet, Convolution with Edge-Node Switching graph neural network, for learning tasks in graph-structured data with both node and edge features. CensNet is a general graph embedding framework, which embeds both nodes and edges to a latent feature space. By using line graph of the original undirected graph, the role of nodes and edges are switched, and two novel graph convolution operations are proposed for feature propagation. Experimental results on real-world academic citation networks and quantum chemistry graphs show that our approach achieves or matches the state-of-the-art performance in four graph learning tasks, including semi-supervised node classification, multi-task graph classification, graph regression, and link prediction.