Chordless Structure: A Pathway to Simple and Expressive GNNs
Hongxu Pan, Shuxian Hu, Mo Zhou, Zhibin Wang, Rong Gu, Chen Tian, Kun Yang, Sheng Zhong
TL;DR
This work identifies chords as an unnecessary source of complexity for cycle-based graph representations and introduces chordless structures as a compact, informative alternative. It presents the Chordless Structure-based Graph Neural Network (CSGNN), whose aggregations over chordless paths and cycles yield expressiveness beyond $KPGNN$ while maintaining polynomial-efficiency. Theoretical analysis positions CSGNN between WL-based limits and higher-order refinements, and experiments on synthetic and real-world datasets show improved accuracy and often reduced computational burden compared to cycle-heavy baselines and 3-WL expressiveness. Overall, the paper offers a principled, scalable route to more expressive GNNs by leveraging and encoding chordless substructures.
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.