[Paper] LightTopoGAT: Enhancing Graph Attention Networks with Topological Features for Efficient Graph Classification

Source: arXiv - 2512.13617v1

Overview

The paper presents LightTopoGAT, a streamlined Graph Attention Network (GAT) that boosts graph‑level classification by explicitly feeding simple topological cues—node degree and local clustering coefficient—into the node embeddings. By doing so, the model captures global structural patterns that vanilla message‑passing GNNs often miss, while keeping the parameter count low enough for practical deployment.

Key Contributions

• Topological augmentation: Introduces degree and clustering coefficient as additional node features, enriching the representation without costly graph‑level pooling.
• Lightweight attention design: Refactors the standard GAT attention mechanism to stay parameter‑efficient, preserving fast inference and low memory footprint.
• Empirical superiority: Demonstrates consistent accuracy gains on three classic benchmarks (MUTAG, ENZYMES, PROTEINS) against strong baselines (GCN, GraphSAGE, vanilla GAT).
• Ablation analysis: Shows that the observed improvements stem directly from the added topological features, confirming their utility.
• Simplicity & reproducibility: The method requires only a few extra input columns and minimal code changes, making it easy to adopt in existing GNN pipelines.

Methodology

1. Feature enrichment: For each node (v) the authors compute two scalar topological descriptors:

   • Degree (\deg(v)) – number of incident edges.
   • Local clustering coefficient (C(v)) – fraction of possible triangles that actually exist around (v).
     These are concatenated to the original node attribute vector, yielding an augmented feature matrix (\mathbf{X}’ = [\mathbf{X},|,\deg,|,C]).

2. Lightweight GAT layer:

   • Uses the standard self‑attention formulation
     [ e_{ij}= \text{LeakyReLU}\big(\mathbf{a}^\top [\mathbf{W}\mathbf{h}_i ,||, \mathbf{W}\mathbf{h}_j]\big) ]
     but reduces the dimensionality of (\mathbf{a}) and shares the linear projection (\mathbf{W}) across heads to cut parameters.
   • Applies softmax over neighbor scores to obtain attention coefficients (\alpha_{ij}) and aggregates neighbor messages as
     [ \mathbf{h}‘i = \sigma!\bigg(\sum{j\in \mathcal{N}(i)} \alpha_{ij}\mathbf{W}\mathbf{h}_j\bigg). ]

3. Graph readout: After stacking 2–3 LightTopoGAT layers, node embeddings are pooled globally (e.g., mean‑pool) to produce a graph‑level vector, which is fed to a simple MLP classifier.

4. Training: Standard cross‑entropy loss with Adam optimizer; no extra regularization beyond dropout.

Results & Findings

• Consistent edge over GCN, GraphSAGE, and vanilla GAT across all three datasets.
• Ablation: Removing degree or clustering coefficient drops performance back to near‑baseline, confirming each descriptor contributes uniquely.
• Parameter count: LightTopoGAT uses ~15 % fewer trainable parameters than a standard 2‑head GAT with comparable hidden size, leading to ~20 % faster training on a single GPU.

Practical Implications

• Low‑resource deployment: The lightweight attention scheme makes the model suitable for edge devices or real‑time inference where memory and latency are tight (e.g., fraud detection on transaction graphs).
• Plug‑and‑play augmentation: Adding degree and clustering coefficient is a one‑line preprocessing step; existing GNN codebases can adopt LightTopoGAT without redesigning the architecture.
• Better global awareness: For domains where graph topology carries domain knowledge—chemistry (molecular rings), bioinformatics (protein interaction motifs), social networks (community structures)—the method can capture patterns that pure attribute‑based GNNs miss.
• Scalable to larger graphs: Because the extra features are computed locally and the attention heads are shared, the approach scales similarly to standard GATs, avoiding the quadratic blow‑up of more complex higher‑order GNNs.

Limitations & Future Work

• Feature simplicity: Only degree and clustering coefficient are used; richer topological descriptors (e.g., betweenness centrality, spectral embeddings) might yield further gains but at higher preprocessing cost.
• Benchmark scope: Experiments are limited to three relatively small, well‑studied datasets; performance on massive, heterogeneous graphs (e.g., web‑scale knowledge graphs) remains untested.
• Static topology: The method assumes a fixed graph structure; dynamic or evolving graphs would require recomputing topological features, which could be costly.
• Future directions suggested by the authors include exploring adaptive weighting of topological vs. attribute information, integrating learned positional encodings, and extending the framework to inductive settings where unseen graph structures appear at test time.

Authors

• Ankit Sharma
• Sayan Roy Gupta

Paper Information

• arXiv ID: 2512.13617v1
• Categories: cs.LG
• Published: December 15, 2025
• PDF: Download PDF