Edge-Level Automorphism in GNNs: A Quantitative Framework and Effective Designs For Link Prediction

2026-09-28

AI Summary

This study addresses the representation collapse in standard Graph Neural Networks (GNNs) caused by node automorphisms, which severely limits link prediction performance. To overcome this, we introduce the first edge-level automorphism analysis framework, proposing the EAR metric and edge orbit theory to formally quantify expressive power. We further design the EO-GNN architecture, which integrates an automorphism-aware dropout mechanism based on Weisfeiler-Lehman hashing with a subgraph orbit-biased aggregation scheme. Extensive experiments demonstrate that EO-GNN improves link prediction performance by 42.36% and 28.44% on synthetic and real-world datasets, respectively, under highly automorphic conditions. These results effectively break through the expressivity bottleneck imposed by structural symmetry, offering a principled solution for enhancing GNNs in symmetric graph domains.

Abstract

Graph Neural Networks (GNNs) are effective for learning node and link embeddings through permutation-equivariant aggregation. However, standard GNNs collapse automorphic nodes, i.e., those with identical structural roles (or orbits) into indistinguishable representations, leading to the node automorphism problem. This collapse limits their expressive power and degrades link prediction performance. Existing approaches to characterize GNN expressiveness rely primarily on Weisfeiler-Lehman (WL) analyses, but these methods are typically qualitative and often misaligned with empirical results. To address this gap, we begin by introducing a novel quantitative framework to assess GNN expressiveness for link prediction. We first formalize edge-level automorphism through edge orbits, which capture the set of structural role pairs for nodes that share a link. Then, we introduce the edge automorphism ratio (EAR), a scalar metric that quantifies a GNN's ability to distinguish links in a given graph. We empirically demonstrate that EAR correlates strongly with performance, validating its practical benefit. Building on this insight, we design EDGE-ORBIT EQUIVARIANT GRAPH NEURAL NETWORK (EO-GNN), a GNN architecture that addresses automorphism collapse while preserving equivariance and incurring minimal computational overhead. EO-GNN accomplishes this through two core designs combined with WL-based node hashes: (i) automorphism-aware dropouts and (ii) subgraph orbit-biased aggregation. Empirical evaluations on synthetic and real graphs show improvements of up to 42.36% and 28.44%, respectively, in predicting links in scenarios with high automorphism.

Problem

• Graph Neural Networks
• Node Automorphism
• Link Prediction
• Expressiveness
• Edge-Level Automorphism

Innovation

• Edge-Level Automorphism
• Edge Automorphism Ratio (EAR)
• EO-GNN
• Link Prediction
• Subgraph Orbit-Biased Aggregation