The citation-based impact of complex innovation systems scales with the size of the system

The aim of this paper is to explore the power-law relationship between the publishing size of complex innovation systems and their citation-based impact. We analyzed articles and reviews from InCites (TM) database published by six complex innovation systems. We found scale-invariant properties in the complex innovation systems which were analyzed. These properties are evidenced in the power law correlation between complex innovation systems' citation-based impact and their size with a scaling exponent alpha approximate to 1.19 +/- 0.01. The results suggest citations to a complex innovation system tend to increase 2(1.19) or 2.28 times when the system doubles its size over time. These scale-invariant emergent properties are a common property of a complex innovation system. These properties can be quantified using the parameters of scale-invariant correlation. These parameters can be used to formulate measures and models useful for informing public policy about scale-invariant emerging properties of a complex innovation system, making comparisons of citation impact between complex systems of vastly different sizes, evaluating citation impact of complex innovation systems according to their size, long range planning, and elaborating rankings across complex innovation systems.