Scientific Collaboration Index (Co-Authorship Intensity)

The Degree of Collaboration is the proportion of papers that have more than one author, a value between 0 and 1 that tells you how common collaboration is but nothing about team size. The Collaboration Index is the average number of authors per paper, which is sensitive to team size and rises as teams grow but is unbounded and can be skewed by a few very large author lists. They answer different questions — prevalence of collaboration versus size of teams — and are best reported together.

Both earlier measures have shortcomings: the Degree of Collaboration ignores team size, and the Collaboration Index is unbounded and dominated by outliers. Lawani and later Ajiferuke, Burell and Tague proposed the Collaborative Coefficient, which weights each paper by the reciprocal of its number of authors so that additional authors increase the index with diminishing returns, while keeping it bounded between 0 and 1. This gives a single measure that distinguishes team sizes yet stays on a comparable, interpretable scale.

Papers with hundreds or thousands of authors — common in high-energy physics, genomics, and large clinical trials — can dominate the mean-based Collaboration Index and distort comparisons. Good practice is to inspect the author-count distribution first, report the bounded Collaborative Coefficient and Degree of Collaboration alongside the mean, and consider trimming, capping, or separately analyzing hyper-authored papers. The right choice depends on the field; the key is to be explicit so the indices remain comparable and not silently driven by a few extreme cases.