Evolutionary Refinement of Generative Graph Topologies: A Hybrid WGAN-GA Approach

2026-05-27

AI Summary

This work addresses the challenge of generating realistic graph data while preserving critical structural properties such as degree distribution and spectral characteristics, which are often distorted in existing methods. The authors propose a novel hybrid approach that integrates Wasserstein GAN (WGAN) with a genetic algorithm (GA). Initially, WGAN produces a coarse graph, which is subsequently refined through GA-based evolutionary optimization of edge connections in a gradient-free manner. Notably, this is the first study to incorporate GA into the post-processing stage of GAN-based graph generation, using Maximum Mean Discrepancy (MMD) as the optimization objective. The method achieves a significant reduction in aggregate MMD metrics, yielding synthetic graphs that closely match real-world data in key topological features while maintaining diversity, thereby enhancing both the quality and practical utility of generated graphs.

Abstract

Generating realistic graph-structured data is challenging due to discrete connectivity, varying graph sizes, and class-specific structural patterns. Recent Generative Adversarial Networks (GAN)-based graph generation methods improve edge modelling by learning connectivity and matching class-specific density distributions. However these models still exhibit noticeable deviations such as in degree and spectral distribution when compared to real graphs, indicating that important structural properties are not fully preserved. This work aims to reduce these deviations by refining the graphs produced by an existing GAN-based graph generator framework with a Genetic Algorithm (GA). In the GAN framework, the generator produces both node features and connectivity patterns, while a GNN-based critic evaluates graph realism and class consistency to ensure global structural and class alignment. Building on this foundation, we apply a GA to refine the edges of generated graphs. The refinement process guides synthetic graphs toward closer agreement with real data, while preserving diversity and novelty. Experimental results show that the GA refinement consistently lowers combined Maximum Mean Discrepancy (MMD) compared to the base model, leading to graphs that more closely match real structural patterns. This demonstrates that evolutionary refinement is an effective and flexible way to correct residual structural deviations in GAN-based graph generators, improving their suitability for realistic graph synthesis and data augmentation.

Problem

• graph generation
• structural deviation
• degree distribution
• spectral distribution
• realistic graph synthesis

Innovation

• evolutionary refinement
• graph generation
• WGAN-GA hybrid
• structural realism
• genetic algorithm