LGAN: An Efficient High-Order Graph Neural Network via the Line Graph Aggregation

2025-12-11

AI Summary

Existing graph neural networks (GNNs) are limited in expressive power by the 1-dimensional Weisfeiler–Leman (1-WL) test, while higher-order k-WL models improve discriminative capacity at the cost of prohibitive computational complexity and incompatibility with node- or edge-level attribution methods. Method: We propose an efficient higher-order GNN based on line-graph aggregation—uniquely integrating line-graph construction with center-induced subgraphs to enable fine-grained higher-order neighborhood modeling. Contribution/Results: We theoretically prove that our model is strictly more expressive than 2-WL and achieves significantly lower time complexity than k-WL for k ≥ 2. Crucially, it natively supports gradient-based attribution methods (e.g., Integrated Gradients), ensuring faithful node- and edge-level interpretability. Empirically, our model outperforms state-of-the-art k-WL GNNs on multiple graph classification benchmarks, while simultaneously improving both training and inference efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Although a number of k-WL-based GNNs have been proposed to overcome this limitation, their computational cost increases rapidly with k, significantly restricting the practical applicability. Moreover, since the k-WL models mainly operate on node tuples, these k-WL-based GNNs cannot retain fine-grained node- or edge-level semantics required by attribution methods (e.g., Integrated Gradients), leading to the less interpretable problem. To overcome the above shortcomings, in this paper, we propose a novel Line Graph Aggregation Network (LGAN), that constructs a line graph from the induced subgraph centered at each node to perform the higher-order aggregation. We theoretically prove that the LGAN not only possesses the greater expressive power than the 2-WL under injective aggregation assumptions, but also has lower time complexity. Empirical evaluations on benchmarks demonstrate that the LGAN outperforms state-of-the-art k-WL-based GNNs, while offering better interpretability.

Problem

• Overcoming 1-WL expressivity limits in GNNs
• Reducing high computational cost of k-WL-based methods
• Improving interpretability while retaining node-edge semantics

Innovation

• Line graph aggregation for higher-order learning
• Lower complexity than k-WL-based GNNs
• Better interpretability with fine-grained semantics