In a graph-level variational graph autoencoder (VGAE), the encoder produces a single latent vector for an entire graph by appending a pooling layer after a GNN. Two separate GNNs parameterize the mean and log-variance of the approximate posterior:

$\mu_{\mathbf{z}_G} = \text{POOL}_{\mu}(\text{GNN}_{\mu}(\mathbf{A}, \mathbf{X}))$

$\log \sigma_{\mathbf{z}_G} = \text{POOL}_{\sigma}(\text{GNN}_{\sigma}(\mathbf{A}, \mathbf{X}))$

where $\text{POOL}: \mathbb{R}^{|V| \times d} \rightarrow \mathbb{R}^{d}$ aggregates node-level embeddings into a single graph-level vector. Unlike the node-level VGAE encoder, this formulation defines a posterior distribution for each entire graph rather than for each individual node.