# Towards Higher-order Topological Consistency for Unsupervised Network Alignment

arXiv: https://arxiv.org/abs/2208.12463 · HTML: https://mlsanity.com/paper/2208.12463/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [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)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [Improving zero-shot learning by mitigating the hubness problem](https://mlsanity.com/paper/1412.6568/) (2014)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Triangular Alignment (TAME): A Tensor-based Approach for Higher-order Network Alignment](https://mlsanity.com/paper/1510.06482/) (2015)
- [GREAT: GRaphlet Edge-based network AlignmenT](https://mlsanity.com/paper/1410.5103/) (2014)

## Built on by (most cited first, 3 of 3)

- [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)
- [NAEx: A Plug-and-Play Framework for Explaining Network Alignment](https://mlsanity.com/paper/2508.04731/) (2025)

## Abstract (arXiv)

Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been attracting more and more attention. However, the topological consistency assumptions defined by existing methods are generally low-order and less accurate because only the edge-indiscriminative topological pattern is considered, which is especially risky in an unsupervised setting. To reposition the focus of the alignment process from low-order to higher-order topological consistency, in this paper, we propose a fully unsupervised network alignment framework named HTC. The proposed higher-order topological consistency is formulated based on edge orbits, which is merged into the information aggregation process of a graph convolutional network so that the alignment consistencies are transformed into the similarity of node embeddings. Furthermore, the encoder is trained to be multi-orbit-aware and then be refined to identify more trusted anchor links. Node correspondence is comprehensively evaluated by integrating all different orders of consistency. {In addition to sound theoretical analysis, the superiority of the proposed method is also empirically demonstrated through extensive experimental evaluation. On three pairs of real-world datasets and two pairs of synthetic datasets, our HTC consistently outperforms a wide variety of unsupervised and supervised methods with the least or comparable time consumption. It also exhibits robustness to structural noise as a result of our multi-orbit-aware training mechanism.