Zipf-Mandelbrot-Pareto model for co-authorship popularity

Abstract

Each co-author (CA) of any scientist can be given a rank (r) of im-portance according to the number (J) of joint publications which the authors have together. In this paper, the Zipf-Mandelbrot-Pareto law, i.e. J ∝ 1/(ν + r)ζ is shown to reproduce the empirical relationship be-tween J and r and shown to be preferable to a mere power law, J ∝ 1/rα. The CA core value, i.e. the core number of CAs, is unaffected, of course. The demonstration is made on data for two authors, with a high number of joint publications, recently considered by Bougrine (2014) and for 7 authors, distinguishing between their ”journal ” and ”proceedings ” pub-lications as suggested by Miskiewicz (2013). The rank-size statistics is discussed and the α and ζ exponents are compared. The correlation co-efficient is much improved ( ∼ 0.99, instead of 0.92). There are marked deviations of such a co-authorship popularity law depending on sub-fields. On one hand, this suggests an interpretation of the parameter ν. On the other hand, it suggests a novel model on the (likely time dependent) struc-tural and publishing properties of research teams. Thus, one can propose a scenario for how a research team is formed and grows. This is based on a hierarchy utility concept, justifying the empirical Zipf-Mandelbrot-Pareto law, assuming a simple form for the CA publication/cost ratio, cr = c0 log2(ν + r). In conclusion, such a law and model can suggest practical applications on measures of research teams. In Appendices, the frequency-size cumulative distribution function is discussed for two sub-fields, with other technicalities

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