Hello I’m currently learning Belief Propagation (Pearl algorithm) in Bayesian Network and encountered this cross-edge graph.

As far as I know, this graph is not a polytree (based on the the definition that its underlying undirected graph is not a tree). However, I wonder if it is singly-connected since there is only at most one path between each pair of nodes if the graph is directed but if converted to undirected there are at most two paths (e.g between V1 and V2) so this becomes multi-connected.

If the latter is the case, can the graph be transformed to the polytree before applying BP using method such as Cutset Conditioning or do I have to use approximate inference technique (e.g: Loopy BP)?

Hope someone can clarify this. Thank you!