# Bermuda Triangles: GNNs Fail to Detect Simple Topological Structures

arXiv: https://arxiv.org/abs/2105.00134 · HTML: https://mlsanity.com/paper/2105.00134/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Multi-Label Image Recognition with Graph Convolutional Networks](https://mlsanity.com/paper/1904.03582/) (2019)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)

## Built on by (most cited first, 1 of 1)

- [A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks](https://mlsanity.com/paper/2605.28578/) (2026)

## Abstract (arXiv)

Most graph neural network architectures work by message-passing node vector embeddings over the adjacency matrix, and it is assumed that they capture graph topology by doing that. We design two synthetic tasks, focusing purely on topological problems -- triangle detection and clique distance -- on which graph neural networks perform surprisingly badly, failing to detect those "bermuda" triangles. Datasets and their generation scripts are publicly available on github.com/FujitsuLaboratories/bermudatriangles and dataset.labs.fujitsu.com.