Neuronal networks show synchronous activity or receive highly synchronous inputs during a variety of different behaviors. Deficits of synchronous activity are associated with impairment of cognition, whereas hypersynchrony can lead to epileptic seizures. Different network mechanisms for synchrony generation have been proposed and studied computationally and experimentally. One such mechanism (interneuron gamma generator, ING) relies solely on recurrent inhibitory interneuron connectivity. The number of inhibitory synapses must be sufficiently large, with the exact number depending on the other neuronal and synaptic parameters of the model. In the dentate gyrus – a hippocampal area central to memory formation – the ING mechanism is thought to be enabled by parvalbumin positive interneurons. Here we incorporate recently published connectivity data of the dentate gyrus into a biophysical computational model to test its ability to generate synchronous activity. We find that recurrent interneuron connectivity is insufficient to induce a synchronous network state. This is the case for the interneuron network itself but also for the broader dentate gyrus circuitry. In the asynchronous state, recurrent interneuron connectivity can have small synchronizing effects for asynchronous input but can also desynchronize the network for some types of synaptic input. Our results show that a synchronizing mechanism relying solely on interneurons is unlikely to be biologically plausible in the dentate gyrus.