Scale-Adjusted Metrics of Scientific Collaboration

Scientific collaboration is increasing on nearly all fronts. In most fields of inquiry, the proportions of multiple authors’, multiple institutions’, and multiple countries’ papers have increased regularly since the birth of scientific journals. Two questions that are frequently asked are: how does collaboration compare from one place to the other, and how does the intensity of collaboration between partners compare in systems with multiple players? For obvious reasons, absolute numbers do not reveal much, but it has been known since the 1970s that the percentages of collaboration present an inverse relationship relative to the number of papers. This paper presents scale-independent methods to examine how frequently collaboration occurs as a function of size. In addition to these scale-adjusted statistics, which are based on the use of the Katz normalization method, this paper proposes a new method to compute a scale-adjusted preference index of collaboration between entities of various sizes. Examples are provided for the world, the European Research Area (ERA), and the US states, as well as for Canadian universities.