The message-passing approach to percolation on networks models averages over infinitely shuffled random ensembles, so its accuracy decreases as networks approach tree structure.
Correctness of Local Probability Propagation in Graphical Models with Loops,
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On the accuracy of message-passing approaches to percolation in complex networks
The message-passing approach to percolation on networks models averages over infinitely shuffled random ensembles, so its accuracy decreases as networks approach tree structure.