Does neural network in brain form cycles?
In general neural networks are a lot less simple and directed than ANNs or artificial circuitry - connections can be inhibitory or excitatory, vary widely in strength etc etc. So unsurprisingly yes, recurrence is observed in actual neural networks. I don't know of any statistics on the frequency of such network structures, or even if such exists. Our knowledge of the brain at this fine level is still limited I think, the more global attempt to map 'the connectome' generally consider things at a higher resolution.