ZipfMandelbrotPareto 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 ZipfMandelbrotPareto 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 (Scientometrics, 98(2): 10471064, 2014) and for seven authors, distinguishing between their journal and proceedings publications as suggested by Miskiewicz (Physica A, 392(20), 51195131, 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 ZipfMandelbrotPareto 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
co-authorship ranking zipfmandelbrotpareto law power laws proceedings research topics peer review journals co-author core