# Graph Edge Representation via Tensor Product Graph Convolutional Representation

arXiv: https://arxiv.org/abs/2406.14846 · HTML: https://mlsanity.com/paper/2406.14846/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [Predicting multicellular function through multi-layer tissue networks](https://mlsanity.com/paper/1707.04638/) (2017)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Attention-based Graph Neural Network for Semi-supervised Learning](https://mlsanity.com/paper/1803.03735/) (2018)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Line Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2010.10046/) (2020)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Automated Self-Supervised Learning for Graphs](https://mlsanity.com/paper/2106.05470/) (2021)
- [Tensor Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/2001.05313/) (2020)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Sparse Graph Attention Networks](https://mlsanity.com/paper/1912.00552/) (2019)
- [Co-embedding of Nodes and Edges with Graph Neural Networks](https://mlsanity.com/paper/2010.13242/) (2020)
- [Label-Consistency based Graph Neural Networks for Semi-supervised Node Classification](https://mlsanity.com/paper/2007.13435/) (2020)
- [Node-wise Localization of Graph Neural Networks](https://mlsanity.com/paper/2110.14322/) (2021)
- [Doubly Contrastive Deep Clustering](https://mlsanity.com/paper/2103.05484/) (2021)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have been widely studied. The core of GCNs is the definition of convolution operators on graphs. However, existing Graph Convolution (GC) operators are mainly defined on adjacency matrix and node features and generally focus on obtaining effective node embeddings which cannot be utilized to address the graphs with (high-dimensional) edge features. To address this problem, by leveraging tensor contraction representation and tensor product graph diffusion theories, this paper analogously defines an effective convolution operator on graphs with edge features which is named as Tensor Product Graph Convolution (TPGC). The proposed TPGC aims to obtain effective edge embeddings. It provides a complementary model to traditional graph convolutions (GCs) to address the more general graph data analysis with both node and edge features. Experimental results on several graph learning tasks demonstrate the effectiveness of the proposed TPGC.