Fractional Variational Graph Autoencoders for Enhancing Non-Local Representation Learning on Graphs

While Graph Autoencoders (GAEs) have become a standard for unsupervised representation learning, their reliance on integer-order convolutions inherently restricts information propagation to immediate local neighborhoods. This paper introduces the Fractional Graph Autoencoder (FGAE) and its variational extension (FVGAE) to move beyond these local constraints. By integrating fractional Laplace operators, our framework generalizes conventional GAEs and enables tunable non-local propagation. We show that the fractional order α acts as a structural regularizer, utilizing the Green’s function of anomalous diffusion to induce a form of structural memory within the latent space. This allows the model to recover long-range dependencies that are typically lost in standard architectures. Systematic benchmarking across eight datasets—ranging from homophilic citation networks to heterophilic and dense product graphs—shows that these fractional variants consistently outperform both foundational and state-of-the-art baselines (ARGA, SIG-VAE, and GraphMAE). Notably, on the Amazon Computers and Citeseer datasets, our methods achieve relative increases in Normalized Mutual Information (NMI) of 77.55% and 67.28%, respectively. Statistical analysis confirms these gains are robust, with large effect sizes (Cohen’s d>0.80) and significance at p<0.05. These findings suggest that fractional graph autoencoding offers a mathematically grounded inductive bias for capturing the complex, multi-scale dynamics of real-world networked systems.