Rank-based distributions in scientific papers affiliations: Different forms of Zipf's law with and without higher order inverse participation ratios

Although often difficult to define and parameterize, scientific collaboration between scientists from different centers and different countries or continents seems to be an interesting and important issue in an increasingly interconnected world. One natural source of such information is scientific papers that include the affiliations of the authors. They do not allow determining the origin of the authors (at least currently), but they can be used to show how large the participation of individual countries in the scientific world is. By analyzing a large set of publications, it is possible to collect chains covering countries and their multiplicity in the affiliations of the authors, and on this basis it is possible to show the most common patterns of collaborating scientific teams. Since in this article we are interested in a more general, statistical approach, the obtained chains are used to calculate an indicator (known as the inverse participation ratio) that expresses different patterns of the distribution of participation of individual countries. We show that the scientific world is another example of universal laws observed in the world because the obtained distribution of inverse participation ratio values obeys Zipf's law.