# WL-Align: Weisfeiler-Lehman Relabeling for Aligning Users across Networks via Regularized Representation Learning

arXiv: https://arxiv.org/abs/2212.14182 · HTML: https://mlsanity.com/paper/2212.14182/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 29 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Multi-level Graph Convolutional Networks for Cross-platform Anchor Link Prediction](https://mlsanity.com/paper/2006.01963/) (2020)
- [G-CREWE: Graph CompREssion With Embedding for Network Alignment](https://mlsanity.com/paper/2007.16208/) (2020)
- [Domain-adversarial Network Alignment](https://mlsanity.com/paper/1908.05429/) (2019)
- [RLINK: Deep Reinforcement Learning for User Identity Linkage](https://mlsanity.com/paper/1910.14273/) (2019)
- [Grad-Align+: Empowering Gradual Network Alignment Using Attribute Augmentation](https://mlsanity.com/paper/2208.11025/) (2022)

## Built on by (most cited first, 7 of 7)

- [Joint Optimal Transport and Embedding for Network Alignment](https://mlsanity.com/paper/2502.19334/) (2025)
- [PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignment](https://mlsanity.com/paper/2505.21366/) (2025)
- [CombAlign: Enhancing Model Expressiveness in Unsupervised Graph Alignment](https://mlsanity.com/paper/2406.13216/) (2024)
- [Centrality-Based Node Feature Augmentation for Robust Network Alignment](https://mlsanity.com/paper/2304.12751/) (2023)
- [Torsion Graph Neural Networks](https://mlsanity.com/paper/2306.13541/) (2023)
- [Network Alignment](https://mlsanity.com/paper/2504.11367/) (2025)
- [Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks](https://mlsanity.com/paper/2605.00725/) (2026)

## Abstract (arXiv)

Aligning users across networks using graph representation learning has been found effective where the alignment is accomplished in a low-dimensional embedding space. Yet, achieving highly precise alignment is still challenging, especially when nodes with long-range connectivity to the labeled anchors are encountered. To alleviate this limitation, we purposefully designed WL-Align which adopts a regularized representation learning framework to learn distinctive node representations. It extends the Weisfeiler-Lehman Isormorphism Test and learns the alignment in alternating phases of "across-network Weisfeiler-Lehman relabeling" and "proximity-preserving representation learning". The across-network Weisfeiler-Lehman relabeling is achieved through iterating the anchor-based label propagation and a similarity-based hashing to exploit the known anchors' connectivity to different nodes in an efficient and robust manner. The representation learning module preserves the second-order proximity within individual networks and is regularized by the across-network Weisfeiler-Lehman hash labels. Extensive experiments on real-world and synthetic datasets have demonstrated that our proposed WL-Align outperforms the state-of-the-art methods, achieving significant performance improvements in the "exact matching" scenario. Data and code of WL-Align are available at https://github.com/ChenPengGang/WLAlignCode.