Given an adjacency matrix $\mathbf{A}$ and node features $\mathbf{X}$, an encoder for node-level latent representations in a Variational Graph Autoencoder (VGAE) uses two separate Graph Neural Networks (GNNs) to generate mean ($\mu_Z$) and variance ($\sigma_Z$) parameters:

$\mu_Z = \text{GNN}_{\mu}(\mathbf{A}, \mathbf{X})$

$\log\sigma_Z = \text{GNN}_\sigma(\mathbf{A}, \mathbf{X})$

where $\mu_Z$ and $\log\sigma_Z$ are $|V| \times d$-dimensional matrices specifying the mean and variance embeddings for each node in the input graph, respectively. After computing $\mu_Z$ and $\log\sigma_Z$, a set of latent node embeddings is sampled using the reparameterization trick:

$Z = \epsilon \circ \exp(\log(\sigma_Z)) + \mu_Z$