Zipf–Mandelbrot–Pareto model for co-authorship popularity

Each co-author (CA) of any scientist can be given a rank $$(r)$$ ( r ) of importance according to the number $$(J)$$ ( J ) of joint publications which the authors have together. In this paper, the Zipf–Mandelbrot–Pareto law, i.e. $$ J \propto 1/(\nu +r)^{\zeta }$$ J ∝ 1 / ( ν + r ) ζ is shown to reproduce the empirical relationship between $$J$$ J and $$r$$ r and shown to be preferable to a mere power law, $$ J \propto 1/r^{\alpha } $$ J ∝ 1 / r α . 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 (Scientometrics, 98(2): 1047–1064, 2014) and for seven authors, distinguishing between their “journal” and “proceedings” publications as suggested by Miskiewicz (Physica A, 392(20), 5119–5131, 2013). The rank-size statistics is discussed and the $$\alpha $$ α and $$\zeta $$ ζ exponents are compared. The correlation coefficient is much improved ( $$\sim $$ ∼ 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 $$\nu $$ ν . On the other hand, it suggests a novel model on the (likely time dependent) structural 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, $$c_r = c_0\, log_2 (\nu +r)$$ c r = c 0 l o g 2 ( 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