Bibliometrics for collaboration works

An important issue in bibliometrics is the weighing of co-authorship in the production of scientific collaborations, which are becoming the standard modality of research activity in many disciplines. The problem is especially relevant in the field of high-energy physics, where collaborations reach 3000 authors, but it can no longer be ignored also in other domains, like medicine or biology. We present theoretical and numerical arguments in favour of weighing the individual contributions as $1/N_{\rm aut}^\alpha$ where $N_{\rm aut}$ is the number of co-authors. When counting citations we suggest the exponent $\alpha\approx 1$, that corresponds to fractional counting. When counting the number of papers we suggest $\alpha \approx 1/3 - 1/2$, with the former (latter) value more appropriate for larger (smaller) collaborations. We expect and verify that the $h$ index scales as the square root of the average number of co-authors, and define a fractionalized $h$ index that does not scale with collaboration size.