# Improving the Expressive Power of Graph Neural Network with Tinhofer Algorithm

arXiv: https://arxiv.org/abs/2104.01848 · HTML: https://mlsanity.com/paper/2104.01848/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 5 Apr 2021.

## Builds on (most cited first, 19 of 19)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)

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

- [Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization](https://mlsanity.com/paper/2506.13911/) (2025)

## Abstract (arXiv)

In recent years, Graph Neural Network (GNN) has bloomly progressed for its power in processing graph-based data. Most GNNs follow a message passing scheme, and their expressive power is mathematically limited by the discriminative ability of the Weisfeiler-Lehman (WL) test. Following Tinhofer's research on compact graphs, we propose a variation of the message passing scheme, called the Weisfeiler-Lehman-Tinhofer GNN (WLT-GNN), that theoretically breaks through the limitation of the WL test. In addition, we conduct comparative experiments and ablation studies on several well-known datasets. The results show that the proposed methods have comparable performances and better expressive power on these datasets.