Given adjacency matrix $A$ and node features $X$, use two separate GNNs to generate mean ($\mu_Z$) and variance ($\sigma_Z$) parameters.

• $\mu_Z =$ GNN$_{\mu}$(A, X)
• log$\sigma_Z$ = GNN$_\sigma$(A, X)

where $\mu_Z$ and log$\sigma_Z$ are |V| x d-dimensional matrices that specify the mean and variance embeddings for each node in input graph, respectively.

Once we have $\mu_Z$ and log$\sigma_Z$, we sample a set of latent node embeddings:

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