Fast neuronal oscillations in gamma frequencies are observed in neocortex and hippocampus during essential arousal behaviors. Through a four-variable Hodgkin-Huxley type model, Wang and Buzsáki have numerically demonstrated that such rhythmic activity can emerge from a random network of GABAergic interneurons via minimum synaptic inputs. In this case, the intrinsic neuronal characteristics and network structure act as the main drive of the rhythm. We investigate inhibitory network synchrony with a low complexity, two-variable adap-tive exponential integrate-and-fire (AdEx) model, whose parameters possess strong physiological relevances, and provide a comparison with the two-variable Izhike-vich model and Morris-Lecar model. Despite the simplicity of these three models, AdEx model shares two important results with the previous biophysically detailed Hodgkin-Huxley type model: the minimum number of synaptic input necessary to initiate network gamma-band rhythms remains the same, and this number is weakly dependent on the network size. Meanwhile, Izhikevich and Morris-Lecar neurons demonstrate different results in this study. We further investigate the necessary neuronal, synaptic and connectivity properties, including gap junctions and shunting inhibitions, for AdEx model leading to sparse and random network synchrony in gamma rhythms and nested theta gamma rhythms. These findings suggest a computationally more tractable framework for studying synchronized networks in inducing cerebral gamma band activities.