Graph link prediction has long been a central problem in graph representation learning in both network analysis and generative modeling. Recent progress in deep learning has introduced increasingly sophisticated architectures for capturing relational dependencies within graph-structured data. In this work, we propose the Generalized Graph Transformer Variational Autoencoder (GGT-VAE). Our model integrates Generalized Graph Transformer Architecture with Variational Autoencoder framework for link prediction. Unlike prior GraphVAE, GCN, or GNN approaches, GGT-VAE leverages transformer style global self-attention mechanism along with laplacian positional encoding to model structural patterns across nodes into a latent space without relying on message passing. Experimental results on several benchmark datasets demonstrate that GGT-VAE consistently achieves above-baseline performance in terms of ROC-AUC and Average Precision. To the best of our knowledge, this is among the first studies to explore graph structure generation using a generalized graph transformer backbone in a variational framework.