Chordless Structure: A Pathway to Simple and Expressive GNNs

2025-05-25

AI Summary

Graph Neural Networks (GNNs) face a fundamental trade-off between expressive power and computational efficiency. Method: This paper proposes the Chordless-Structure-Guided GNN (CSGNN), the first model to systematically identify chord edges as both expressively redundant and computationally costly—thereby eliminating them to focus exclusively on essential cycle structures. CSGNN employs chordless graph structure extraction and cycle-aware message passing. Contribution/Results: It achieves strictly stronger expressivity than any k-hop GNN, retains polynomial-time complexity, and surpasses the 3-WL test in graph discrimination. Empirically, CSGNN attains superior performance with lower inference overhead across multiple real-world graph benchmarks—providing the first empirical validation that high expressivity and low computational cost are simultaneously attainable in GNN design.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Enhancing GNN expressiveness without high computational cost
• Reducing graph complexity by omitting non-essential chord information
• Proposing CSGNN for better performance and lower computational expense

Innovation

• Chordless structures simplify GNN design
• CSGNN enhances expressiveness with polynomial complexity
• CSGNN outperforms 3-WL GNNs efficiently