To address the unknown node ordering in graph-level variational decoders, we can compute the likelihood for each possible node ordering and select the one that maximizes the likelihood: $p_{\theta}(G | \mathbf{z}_G) = \max_{\pi\in\Pi}\prod_{(u,v)\in \mathcal{V}} \tilde{A}^{\pi}[u,v] A[u,v]+(1-\tilde{A}^{\pi}[u,v]) (1-A[u,v])$ where $\tilde{A}^{\pi}$ is the predicted adjacency matrix using a specific node ordering $\pi$. The main drawback of this approach is that it is computationally expensive.