WL-SeqVAE: Sequence-Based Graph Generation Using Variational Autoencoders and Weisfeiler-Leman Colors

Abstract

In this paper, we introduce WL-SeqVAE, a sequence-based variational autoencoder for generating graphs. The key observation behind WL-SeqVAE is that node colors induced by the Weisfeiler-Leman (WL) algorithm provide compact discrete summaries of local graph structure and can therefore serve as structural tokens for generation. Rather than learning a distribution over adjacency matrices directly, our method maps each graph to a sequence of WL colors and employs a variational autoencoder that encodes this sequence into a Gaussian latent distribution, from which an autoregressive decoder reconstructs the graph. During generation, compatibility constraints derived from the WL colors guide node and edge predictions, combining global information from the latent representation with local structural consistency. This formulation turns graph generation into a sequence generation problem and avoids directly parameterizing a quadratic adjacency matrix. We evaluate WL-SeqVAE on molecular and general graph generation tasks. Across the evaluated datasets, WL-SeqVAE is competitive with established baselines on several local structural and molecular quality metrics. Code is available at https://github.com/iakovosevdaimon/WL-SeqVAE