Do 'altmetric mentions' follow Power Laws? Evidence from social media mention data in Altmetric.com

Abstract: Power laws are a characteristic distribution that are ubiquitous, in that they are found almost everywhere, in both natural as well as in man-made systems. They tend to emerge in large, connected and self-organizing systems, for example, scholarly publications. Citations to scientific papers have been found to follow a power law, i.e., the number of papers having a certain level of citation x are proportional to x raised to some negative power. The distributional character of altmetrics has not been studied yet as altmetrics are among the newest indicators related to scholarly publications. Here we select a data sample from the altmetrics aggregator Altmetrics.com containing records from the platforms Facebook, Twitter, News, Blogs, etc., and the composite variable Alt-score for the period 2016. The individual and the composite data series of 'mentions' on the various platforms are fit to a power law distribution, and the parameters and goodness of fit determined using least squares regression. The log-log plot of the data, 'mentions' vs. number of papers, falls on an approximately linear line, suggesting the plausibility of a power law distribution. The fit is not very good in all cases due to large fluctuations in the tail. We show that fit to the power law can be improved by truncating the data series to eliminate large fluctuations in the tail. We conclude that altmetric distributions also follow power laws with a fairly good fit over a wide range of values. More rigorous methods of determination may not be necessary at present.