LightTopoGAT: Efficient Topological GAT

• The paper demonstrates that incorporating node degree and clustering coefficients into a two-layer GAT significantly boosts classification accuracy with only a 2.4% parameter overhead.
• The methodology augments standard node features with low-cost topological metrics and employs multi-head attention and mean pooling to efficiently capture both local and global graph structures.
• Empirical results on benchmark datasets like MUTAG, ENZYMES, and PROTEINS reveal that LightTopoGAT outperforms baseline models such as GCN and GraphSAGE in accuracy while maintaining computational efficiency.

LightTopoGAT is a parameter-efficient graph attention network (GAT) tailored for graph classification. Leveraging topological augmentation, LightTopoGAT enriches standard node feature matrices with node degree and local clustering coefficient—structural descriptors encoding both global graph connectivity and local community density. This approach addresses the limitations of conventional message-passing GNNs, particularly their restricted sensitivity to global structures and the challenge of maintaining computational efficiency. LightTopoGAT demonstrates empirically superior performance over established GNN variants with minimal parameter overhead, substantiating the effectiveness of lightweight topological fusion for graph representation learning (Sharma et al., 15 Dec 2025).

1. Motivation and Principal Challenges

Graph neural networks such as GCN, GraphSAGE, and GAT are proficient at capturing local node relationships through message passing yet commonly exhibit two deficiencies: limited capacity for encoding higher-order or global graph structures, and increased computational burden when augmented for expressive power. Conventional message-passing aggregates immediate neighborhood information, potentially omitting macroscopic structural phenomena such as hubs or community segmentation. Enhancements via deeper or more intricate networks often incur substantial parameter growth and inference time, which is suboptimal for deployment in resource-constrained settings.

LightTopoGAT addresses these challenges by introducing topological descriptors—node degree ($d_i$) and local clustering coefficient ($C_i$)—as low-cost features encoding essential structural information. These augmentations provide signals orthogonal to standard node attributes: $d_i$ quantifies node importance in the network, while $C_i$ reflects local density and connectivity patterns. Crucially, both features are computable in time linear in the number of edges, circumventing the computational overhead of more elaborate structural embeddings.

2. Model Architecture and Mathematical Formulation

LightTopoGAT adopts a two-layer GAT backbone augmented via a preprocessing step whereby each node’s degree and local clustering coefficient are concatenated to its feature vector. Formally, for each node $i$ with neighbor set $\mathcal{N}(i)$,

• Degree is given by $d_i = \sum_{j \in \mathcal{N}(i)} 1$
• Local clustering coefficient is $$C_i = \frac{2 \times |\{(j,k): j,k \in \mathcal{N}(i),\, (j,k) \in E\}|}{d_i(d_i - 1)}$$

The augmented node feature is then $$\tilde{x}_i = [x_i \, \|\, d_i \,\|\, C_i] \in \mathbb{R}^{d+2}$$.

This feature matrix proceeds through:

• Layer 1: Multi-head attention ($K=4$ heads) over augmented features.
• Layer 2: Single-head attention with shared weights.
• Mean global pooling to yield graph embedding $h_G$.
• Linear layer and softmax for classification.

3. Attention Mechanism and Lightweight Design

The attention mechanism processes the augmented features $\tilde{x}_i$ using a linear transformation $W \in \mathbb{R}^{F' \times (d+2)}$. For node $i$ and neighbor $j$, attention logits are computed by

$$e_{ij} = \mathrm{LeakyReLU} (a^T [W \tilde{x}_i \, \|\, W \tilde{x}_j])$$

with normalized attention coefficients

$$a_{ij} = \frac{\exp(e_{ij})}{\sum_{k \in \mathcal{N}(i)} \exp(e_{ik})}$$

and node embedding in the head

$$h_i = \sum_{j \in \mathcal{N}(i)} a_{ij}\,W\,\tilde{x}_j$$

Notably, the design preserves architectural simplicity: a single shared weight matrix in the second (single-head) layer and addition of only two scalar features per node. No additional MLPs, gating, or further parameterized mechanisms are introduced. This maintains the computational profile comparable to SimpleGAT but with heightened expressiveness.

4. Parameter Efficiency and Comparative Analysis

LightTopoGAT’s topological augmentation increases parameter count by only 64 relative to the baseline two-layer GAT, constituting approximately 2.4% overhead. Table below summarizes parameter counts (MUTAG dataset; similar for ENZYMES, PROTEINS):

Model	Layer Setup	Params
GCN	2-layer	4,802
GraphSAGE	2-layer	9,346
SimpleGAT	4-head → 1-head	2,690
LightTopoGAT	4-head → 1-head	2,754

Thus, LightTopoGAT achieves 42% fewer parameters than GCN and 70% fewer than GraphSAGE, while delivering improved accuracy (Sharma et al., 15 Dec 2025). This configuration substantiates the claim that topological augmentation yields an advantageous balance between complexity and representational capacity.

5. Training Protocol

Training is conducted via graph-level negative log-likelihood (NLL) loss on softmax outputs. The Adam optimizer with learning rate $0.005$ is employed; dropout ($p=0.5$) is applied between attention layers. Datasets (MUTAG, ENZYMES, PROTEINS) utilize an 80/20 train/test split, 50 epochs, batch size 32, and five independent random seeds (100–104). Early stopping is intentionally omitted, with model selection based on best validation accuracy per run.

6. Empirical Performance and Ablation Analysis

Experiments on TU Dortmund benchmarks confirm LightTopoGAT’s empirical superiority over baselines (GCN, GraphSAGE, SimpleGAT), reporting mean test accuracy ($\pm$ std) over five runs:

Dataset	GCN	GraphSAGE	SimpleGAT	LightTopoGAT
MUTAG	68.95%±7.33	71.58%±8.39	68.42%±3.72	76.32%±7.25
ENZYMES	25.00%±4.59	27.33%±4.10	21.36%±3.17	27.67%±5.90
PROTEINS	69.33%±9.14	67.17%±3.19	67.80%±3.28	71.12%±1.72

LightTopoGAT delivers a 6.6% accuracy increase (MUTAG), 1.3% on ENZYMES, and 2.2% on PROTEINS relative to top-performing baselines.

Ablation studies demonstrate that these improvements stem solely from topological augmentation. Removing degree and clustering coefficient features (LightTopoGAT_NoTopo) causes performance to revert to baseline SimpleGAT:

Dataset	With Topology	No Topology	Delta
MUTAG	76.32%	68.42%	–7.9 points
ENZYMES	27.67%	21.36%	–6.3 points
PROTEINS	71.12%	69.60%	–1.5 points

This confirms the functional utility of the structural features for accurate classification.

7. Applications and Prospective Development

LightTopoGAT achieves an overview of efficiency and expressivity suitable for domains where model compactness and inference speed are critical, such as mobile or IoT inference. The method provides a template for integrating additional, potentially more sophisticated topological features (e.g., betweenness centrality, PageRank) and for adaptive feature selection per dataset characteristics. Potential future research directions include scalability evaluation on large-scale graphs, development of feature weighting mechanisms, and deployment in real-time or edge computing scenarios.

In summary, LightTopoGAT substantiates that minimal topological augmentation within a streamlined GAT architecture can markedly enhance the representation power and classification accuracy of graph neural networks, bridging the gap between local message-passing and global structure modeling without elevating computational overhead (Sharma et al., 15 Dec 2025).