Evolutionary Biological Data Science Laboratory

h-index

The h-index (Hirsch 2005) is the most important personal impact factor one needs to be familiar with, not because it is necessarily the best, but because (1) it was the first major index of its type and most of the other indices are based on it in some way, and (2) it is the single factor with which most other people (e.g., administrators) are likely to be somewhat familiar. You may find another index which you prefer, but everything starts with h.

The h-index is defined as the largest value for which h publications have at least h citations. Put another way, a scientist has an impact factor of h if h of their publications have at least h citations and the other P - h publications have ≤ h citations. Note that h is measured in publications. In formal notation, one might write

$$h=\underset{i}{\max}\left(i\leq C_i\right).$$

These top h publications are often referred to as the “Hirsch core.”

One way to graphically visualize h is to imagine a plot of citation count versus rank for all publications (often called the citation curve). An alternative way of thinking of this is a plot of minimum number of citations for a publication in the top i publications vs. i. By definition, this plot will generally trend from upper left (highest ranked publications with most citations, to lower right (lowest ranked publications with fewest citations), depending on the precise citation distribution of the author. If one were to add a (threshold) line with a slope of one to this plot, the point where the threshold line crosses the citation curve (truncated to an integer) is h. Alternatively, one can visualize h as the size (length of sides) of the largest (integer) square that one can fit under the citation curve.

Example

Publications are ordered by number of citations, from highest to lowest.

Citations (Ci)	47	26	19	15	11	10	4	3	2	1	1	1	1	0	0	0	0	0
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
						h = 6

The largest rank where i ≤ C_i is 6.

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