Feature-Enhanced Graph Neural Networks for Classification of Synthetic Graph Generative Models: A Benchmarking Study

The ability to discriminate between generative graph models is critical to understanding complex structural patterns in both synthetic graphs and the real-world structures that they emulate. While Graph Neural Networks (GNNs) have seen increasing use to great effect in graph classification tasks, few studies explore their integration with interpretable graph theoretic features. This paper investigates the classification of synthetic graph families using a hybrid approach that combines GNNs with engineered graph-theoretic features. We generate a large and structurally diverse synthetic dataset comprising graphs from five representative generative families, Erdos-Renyi, Watts-Strogatz, Barab'asi-Albert, Holme-Kim, and Stochastic Block Model. These graphs range in size up to 1x10^4 nodes, containing up to 1.1x10^5 edges. A comprehensive range of node and graph level features is extracted for each graph and pruned using a Random Forest based feature selection pipeline. The features are integrated into six GNN architectures: GCN, GAT, GATv2, GIN, GraphSAGE and GTN. Each architecture is optimised for hyperparameter selection using Optuna. Finally, models were compared against a baseline Support Vector Machine (SVM) trained solely on the handcrafted features. Our evaluation demonstrates that GraphSAGE and GTN achieve the highest classification performance, with 98.5% accuracy, and strong class separation evidenced by t-SNE and UMAP visualisations. GCN and GIN also performed well, while GAT-based models lagged due to limitations in their ability to capture global structures. The SVM baseline confirmed the importance of the message passing functionality for performance gains and meaningful class separation.