The message-passing approach to percolation on networks models averages over infinitely shuffled random ensembles, so its accuracy decreases as networks approach tree structure.
Heterogeneous micro-structure of percolation in sparse networks,
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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.