When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble.. If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium... Such oscillations do not normally occur in probabilistic networks... which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network.

p. 195 - Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988