The basic GAN-based approach is similar to the graph-level VAE. For instance, for the generator, we can employ a simple multi-layer perceptron (MLP) to generate a matrix of edge probabilities given a seed vector z: $\tilde{A}=\sigma(MLP(z))$.

Given this matrix of edge probabilities, we can then generate a discrete adjacency matrix $\hat{A} \in Z^{|V| x |V|}$ by sampling independent Bernoulli variables for each edge, and the probabilities are given by the entries of $\tilde{A}$.

For the discriminator, we can employ any GNN-based graph classification model. The generator model and the discriminator model can be trained according to this equation using standard tools for GAN optimization.