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

TL;DR

LGAN introduces a high-order GNN using line graph aggregation, achieving greater expressivity and interpretability with lower computational cost compared to existing k-WL-based models.

Contribution

The paper proposes LGAN, a novel high-order GNN that constructs line graphs for better expressivity and interpretability, with proven theoretical advantages and improved empirical performance.

Findings

LGAN outperforms state-of-the-art k-WL-based GNNs on benchmark datasets.

LGAN has greater expressive power than 2-WL under certain conditions.

LGAN offers better interpretability due to fine-grained semantics retention.

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.