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

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.

Adaptive Edge Learning for Density-Aware Graph Generation

Generating realistic graph-structured data is challenging due to discrete structures, variable sizes, and class-specific connectivity patterns that resist conventional generative modelling. While recent graph generation methods employ generative adversarial network (GAN) frameworks to handle permutation invariance and irregular topologies, they typically rely on random edge sampling with fixed probabilities, limiting their capacity to capture complex structural dependencies between nodes. We propose a density-aware conditional graph generation framework using Wasserstein GANs (WGAN) that replaces random sampling with a learnable distance-based edge predictor. Our approach embeds nodes into a latent space where proximity correlates with edge likelihood, enabling the generator to learn meaningful connectivity patterns. A differentiable edge predictor determines pairwise relationships directly from node embeddings, while a density-aware selection mechanism adaptively controls edge density to match class-specific sparsity distributions observed in real graphs. We train the model using a WGAN with gradient penalty, employing a GCN-based critic to ensure generated graphs exhibit realistic topology and align with target class distributions. Experiments on benchmark datasets demonstrate that our method produces graphs with superior structural coherence and class-consistent connectivity compared to existing baselines. The learned edge predictor captures complex relational patterns beyond simple heuristics, generating graphs whose density and topology closely match real structural distributions. Our results show improved training stability and controllable synthesis, making the framework effective for realistic graph generation and data augmentation. Source code is publicly available at https://github.com/ava-12/Density_Aware_WGAN.git.