Before revision:  Using systematic simulations , we propose a parsimonious (three-parameter) model of these ratess-R\'enyi } and  show that different wellknown network families map onto distinct regions of the parameter space of this model.
After revision:  We use extensive simulations over Regular, Erd\H{os-R\'enyi } and show that different wellknown network families map onto distinct regions of the parameter space of this model.