# Effective Decoding in Graph Auto-Encoder using Triadic Closure

arXiv: https://arxiv.org/abs/1911.11322 · HTML: https://mlsanity.com/paper/1911.11322/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2019.

## Built on by (most cited first, 13 of 13)

- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [A Comprehensive Survey on Community Detection with Deep Learning](https://mlsanity.com/paper/2105.12584/) (2021)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [Graph Neural Networks in IoT: A Survey](https://mlsanity.com/paper/2203.15935/) (2022)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Graph Force Learning](https://mlsanity.com/paper/2103.04344/) (2021)
- [On Generalization of Graph Autoencoders with Adversarial Training](https://mlsanity.com/paper/2107.02658/) (2021)
- [Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Views](https://mlsanity.com/paper/2308.10077/) (2023)
- [ResVGAE: Going Deeper with Residual Modules for Link Prediction](https://mlsanity.com/paper/2105.00695/) (2021)
- [New Frontiers in Graph Autoencoders: Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2211.08972/) (2022)
- [Learning Network Representations with Disentangled Graph Auto-Encoder](https://mlsanity.com/paper/2402.01143/) (2024)
- [Masked AutoEncoder for Graph Clustering without Pre-defined Cluster Number k](https://mlsanity.com/paper/2401.04741/) (2024)
- [TFWaveFormer: Temporal-Frequency Collaborative Multi-level Wavelet Transformer for Dynamic Link Prediction](https://mlsanity.com/paper/2603.03963/) (2026)

## Abstract (arXiv)

The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph structure by only considering two nodes at a time, thus ignoring possible interactions among edges. On the other hand, structured prediction, which considers the whole graph simultaneously, is computationally expensive. In this paper, we utilize the well-known triadic closure property which is exhibited in many real-world networks. We propose the triad decoder, which considers and predicts the three edges involved in a local triad together. The triad decoder can be readily used in any graph-based auto-encoder. In particular, we incorporate this to the (variational) graph auto-encoder. Experiments on link prediction, node clustering and graph generation show that the use of triads leads to more accurate prediction, clustering and better preservation of the graph characteristics.