Scaling invariance in a social network with limited attention and innovation

Competition for limited attention in a social network with innovation is investigated. We consider the case where each piece of information has a fitness as proxy of its quality. The higher is the quality the higher are the chances of being transmitted. We describe the behavior of the diversity of information in a social network as a function of time by using scaling arguments and we demonstrate its scaling invariant with respect of time as well as information load, attention and network sizes. Scaling transformations are used to overlap different curves of diversity, obtained by distinct parameters, onto an universal plot.