The message-passing approach to percolation on networks models averages over infinitely shuffled random ensembles, so its accuracy decreases as networks approach tree structure.
Message-Passing Meth- ods for Complex Contagions,
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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.