# Automorphic Equivalence-aware Graph Neural Network

arXiv: https://arxiv.org/abs/2011.04218 · HTML: https://mlsanity.com/paper/2011.04218/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Subgraph Permutation Equivariant Networks](https://mlsanity.com/paper/2111.11840/) (2021)
- [A Network Science perspective of Graph Convolutional Networks: A survey](https://mlsanity.com/paper/2301.04824/) (2023)
- [Inference-friendly Graph Compression for Graph Neural Networks](https://mlsanity.com/paper/2504.13034/) (2025)
- [Edge-Level Automorphism in GNNs: A Quantitative Framework and Effective Designs For Link Prediction](https://mlsanity.com/paper/2609.34729/) (2026)

## Abstract (arXiv)

Distinguishing the automorphic equivalence of nodes in a graph plays an essential role in many scientific domains, e.g., computational biologist and social network analysis. However, existing graph neural networks (GNNs) fail to capture such an important property. To make GNN aware of automorphic equivalence, we first introduce a localized variant of this concept -- ego-centered automorphic equivalence (Ego-AE). Then, we design a novel variant of GNN, i.e., GRAPE, that uses learnable AE-aware aggregators to explicitly differentiate the Ego-AE of each node's neighbors with the aids of various subgraph templates. While the design of subgraph templates can be hard, we further propose a genetic algorithm to automatically search them from graph data. Moreover, we theoretically prove that GRAPE is expressive in terms of generating distinct representations for nodes with different Ego-AE features, which fills in a fundamental gap of existing GNN variants. Finally, we empirically validate our model on eight real-world graph data, including social network, e-commerce co-purchase network, and citation network, and show that it consistently outperforms existing GNNs. The source code is public available at https://github.com/tsinghua-fib-lab/GRAPE.