We can order the nodes using some heuristic node ordering. For example, we can use depth-first search and breadth first-search and order from the highest degree nodes:

$p_{\theta}(G | \mathbf{z}_G) \approx \prod_{(u,v)\in \mathcal{V}} \tilde{A}^{\pi}[u,v] A[u,v]+(1-\tilde{A}^{\pi}[u,v]) (1-A[u,v])$

Or we can also consider a small heuristic set of ordering and average over these orderings:

$p_{\theta}(G | \mathbf{z}_G) \approx \sum_{\pi_i\in\{\pi_1,…\pi_n\}}\prod_{(u,v)\in \mathcal{V}} \tilde{A}^{\pi_i}[u,v] A[u,v]+(1-\tilde{A}^{\pi_i}[u,v]) (1-A[u,v])$

This method has been proven to work great in practice.