Adaptive Edge Learning for Density-Aware Graph Generation

TL;DR

This work tackles realistic generation of class-conditioned graphs with variable sizes. It introduces a density-aware conditional graph generation framework that replaces random edge sampling with a learnable distance-based edge predictor and enforces class-specific sparsity via a top-k density-aware edge selection mechanism within a Wasserstein GAN framework. A GCN-based critic and per-node latent vectors enable stable training and faithful replication of structural patterns, both locally and globally. Experiments on MUTAG, ENZYMES, and PROTEINS show improved distributional fidelity across degree, clustering, and spectral properties, along with high uniqueness and novelty, enabling effective graph-based data augmentation and privacy-preserving synthesis.

Abstract

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.

Figures (1)

• Figure 1: Model overview: the generator produces diverse node features from individual noise vectors combined with class embeddings. The distance-based edge predictor learns to map nodes into a latent space where proximity determines connectivity. Edge selection follows class-specific density statistics extracted from training data. The GNN-based critic processes graphs through multiple convolution layers, pools node features, and combines them with class embeddings to produce Wasserstein scores that ensure both distributional similarity and class alignment. Note that blue represents learning modules. In this approach, the probability distribution remains fully differentiable, allowing the predictor to learn directly from the WGAN objective.