An Efficient Loop and Clique Coarsening Algorithm for Graph Classification

TL;DR

Graph classification with Graph Transformers often treats graph structure as ancillary guidance rather than explicit edge representations. The paper introduces LCC4GC, a linear-time Loop and Clique Coarsening approach that condenses loops and cliques into hypernodes to form a coarsened view, complemented by a line-graph conversion view to incorporate edge-centric information. Three views—original, coarsened, and line-graph—are learned with a GT backbone (U2GNN) and concatenated for final prediction, achieving state-of-the-art performance across eight real-world datasets and 31 baselines. Through extensive ablations, the authors demonstrate the crucial roles of both the LCC and LGC components, as well as the benefits of edge-centric position information, while maintaining practicality through linear-time complexity. The work suggests promising directions for dynamic graphs and broader higher-level structures in graph representation learning.

Abstract

Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central perspectives and lacks explicit representations of edges and structures. One natural question arises as to whether we can leverage a hypernode to represent some structures. Through experimental analysis, we explore the feasibility of this assumption. Based on our findings, we propose an efficient Loop and Clique Coarsening algorithm with linear complexity for Graph Classification (LCC4GC) on GT architecture. Specifically, we build three unique views, original, coarsening, and conversion, to learn a thorough structural representation. We compress loops and cliques via hierarchical heuristic graph coarsening and restrict them with well-designed constraints, which builds the coarsening view to learn high-level interactions between structures. We also introduce line graphs for edge embeddings and switch to edge-central perspective to alleviate the impact of coarsening reduction. Experiments on eight real-world datasets demonstrate the improvements of LCC4GC over 31 baselines from various architectures.

Figures (7)

• Figure 1: Pre-experiment on a toy molecule graph set, which shows four graphs with different features, all containing a benzene ring. (B) illustrates the pairwise comparison between four graphs. (C) presents the comparison between the graph and its coarsening view. We leverage two measurements of Euclidean Distance (bar plots, lower for closer) and Cosine Similarity (line plots, higher for closer) to reveal the latent relations between graphs.
• Figure 2: Overview of our work. (A) The framework of LCC4GC. LCC contains two procedures: (B) clique coarsening and (C) loop coarsening. We design two constraints, hierarchy depth, and loop length, to control the graph coarsening process. (D) An example of how LCC and LGC work.
• Figure 3: LGC workflow. (A) shows the line graph conversion with hard coarsening examples. (B) illustrates how the input graphs with different position information are distinguished by LGC but not LCC.
• Figure 4: Hyper-parameters Study. We evaluate four hyper-parameters: hierarchy depth $K$, the number of Transformer Encoder layers $T$, the number of sampling neighbors $N$, and the hidden size $|H|$.
• Figure 5: Runtimes of all coarsening algorithms. We make logarithmic processing due to different scales of datasets.

Theorems & Definitions (3)

• Definition 1: Loop
• Definition 2: Clique
• Definition 3: Line Graph