A preliminary investigation on diffusion through a layered system

We introduce layered systems such as the citations–citing authors–citing institutes–citing countries one. Diffusion of scientific ideas flows through such layered systems. Our contribution contains three main topics: a fractional counting system for the number of different units in a layer; the fractional number of items of the same type, i.e. in the same layer, over which ideas have been diffused; and the evenness of diffusion over different layers. In this way we construct a coherent system to measure the extent to which scientific ideas are diffused.