Chordless Structure: A Pathway to Simple and Expressive GNNs

TL;DR

This paper introduces a chordless structure approach for GNNs, which simplifies graph representation and enhances expressiveness, leading to better performance and efficiency compared to existing methods.

Contribution

The paper proposes the CSGNN model based on chordless structures, proving its superior expressiveness over k-hop GNNs with lower computational complexity.

Findings

CSGNN outperforms existing GNNs on real-world datasets.

CSGNN achieves better results than 3-WL expressive GNNs.

Chordless structures improve efficiency and effectiveness in graph representation.

Abstract

Researchers have proposed various methods of incorporating more structured information into the design of Graph Neural Networks (GNNs) to enhance their expressiveness. However, these methods are either computationally expensive or lacking in provable expressiveness. In this paper, we observe that the chords increase the complexity of the graph structure while contributing little useful information in many cases. In contrast, chordless structures are more efficient and effective for representing the graph. Therefore, when leveraging the information of cycles, we choose to omit the chords. Accordingly, we propose a Chordless Structure-based Graph Neural Network (CSGNN) and prove that its expressiveness is strictly more powerful than the k-hop GNN (KPGNN) with polynomial complexity. Experimental results on real-world datasets demonstrate that CSGNN outperforms existing GNNs across various graph tasks while incurring lower computational costs and achieving better performance than the GNNs of 3-WL expressiveness.