Zipf-Mandelbrot-Pareto model for co-authorship popularity

Each co-author (CA) of any scientist can be given a rank ($r$) of importance according to the number ($J$) of joint publications which the authors have together. In this paper, the Zipf-Mandelbrot-Pareto law, i.e. $J \propto 1/(\nu+r)^{\zeta}$ is shown to reproduce the empirical relationship between $J$ and $r$ and shown to be preferable to a mere power law, $J \propto 1/r^{\alpha}$. 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" publications as suggested by Miskiewicz (2013). The rank-size statistics is discussed and the $\alpha$ and $\zeta$ 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 $\nu$. 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, $c_r = c_0\: log_2 (\nu+r)$. 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