A scaling between Impact Factor and uncitedness

The Impact Factor has become a well-known measure of the average citation number of articles published in a scientific journal. A journal with a high Impact Factor is assumed to have a low percentage of uncited articles. We show that the scaling relation between the Impact Factor and the uncited percentage can be understood by a simple mechanism. The empirical data can be reproduced by a random mechanism with the cumulative advantage. To further explore the robustness of such a mechanism, we investigate the relation between the average citation number and the uncited percentage from different perspectives. We apply the idea of Impact Factor to the publications of an institute in addition to its general application to the publications of a journal. We find that the same scaling relation can be obtained. We also show that a static relation can be applied to describe the time evolution of a dynamical process. These results provide further justification for the same citation mechanism behind different research fields.