The fractal dimension of a citation curve: quantifying an individual’s scientific output using the geometry of the entire curve

Abstract

Assorted bibliometric indices have been proposed leading to ambiguity in choosing the appropriate metric for evaluation. On the other hand, attempts to fit universal distribution patterns to scientific output have not converged to unified conclusions. To this end, we introduce the concept of fractal dimension to further examine the citation curve of an author. The fractal dimension of the citation curve could provide insight in its shape and form, level of skewness and distance from uniformity as well as the existing publishing patterns, without a priori assumptions on the particular citation distribution. It is shown that the notion of fractal dimension is not correlated to other well-known bibliometric indices. Further, a thorough experimentation of the fractal dimension is presented by using a set of 30,000 computer scientists and more than 9 million publications with over 38 million citations. The distinguishing power of the fractal dimension is investigated when comparing the impact of scientists and when trying to identify award winning scientists in their respective fields.