Quantifying a researcher’s impact: The h-index

There are a growing number of ways in which researchers/academicians are required to provide information on the scholarly output in connection with their career advancement or award of financial assistance. In recent years, scientometric indicators such as impact factor (IF), citation and citation index have become a prerequisite for a researcher or a professional seeking placement. The University Grants Commission (UGC) focuses publications in impact factor journal and number of citations of publications for academic evaluation. Currently a scientometric indicator called h-index has gained popularity and recognition in the assessment of research output. Today, it has rapidly become a widely used measure of a researcher’s scientific output.

What is the h-index?
H-index stands for Hirsch index. The h-index is named after its inventor, physicist Jorge E Hirsch, who proposed it in 2005 as a means of bringing some rigour to the confusing question of who is most deserving of a grant or post. The h-index is a measure of an individual’s scientific research out put. According to Hirsch, “A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np - h) papers have no more than h citations each”. (Source: Hirsch JE. An index to quantify an individual's scientific research output. Proc Natl Acad Sci USA 2005 Nov 15; 102(46):16569-72)

How is h-index calculated?
The h-index expresses the journal's number of papers (h) that have received at least h citations. An individual has an index of h, if h papers have at least h citations each. Thus, the h-index reflects both the number of publications and the number of citations per publication. This index translates the impact (the number of citations) and the scope (the number of papers) of a scientist's work into a straight number. For example, if your h-index is 6, it means that you have 6 papers that have been cited at least 6 times. You may have more papers, suppose 14 papers, only 6 of these papers are cited at least 6 times by other researchers, indicating that other 8 papers have 6 or less than 6 citations. The h-index will reach 7, only if 7 papers receive a minimum of 7 citations.

However, one should cite the database source from which the h-index was derived. It depends which database you use: Web of Science (Thomson ISI), Scopus (Elsevier) or Google Scholar. Each database considers only those citations in the journals listed in each of the database. Web of Science and Scopus use their own selection of the estimated more than 10,000 scientific journals in circulation. The web of Science is not an open access database. Scopus allows viewing your only h-index (without Scopus account). The Google Scholar search engine takes into account reports, grey literature, pre-prints and theses, which results in considerably higher h-indices. In general, it is found that Google Scholar gives a higher h-index for the same researcher when compared to other two databases. Google Scholar is the only one of the three that is freely accessible to the general public. One can easily create Homepage of Google Scholar citation by signing in Gmail account that automatically calculates and updates h-index and its metrics.

Because of the advantages that the h-index offers as a scientometric tool, the h-index has found widespread acceptance. The h-index has become a critical performance parameter. Researchers' importance is measured by their h score. Today no academic bio-data is complete without it. However, some critical objections to the h-index have been raised. It is generally recognized that the main disadvantage of the h-index is its insensitivity to one or several (even outstandingly) highly cited papers. For example, a researcher with total 375 citations may have an h-index of 4 because only 4 of his/her papers have received 4 or more citations; while another researcher with total only 27 citations may have an h-index of also 4 because 4 of his/her papers has received a minimum of 4 citations.

Table 1: Sample example of h-index and g-index of a researcher

Paper rank	Citations(Ci)	Cumulative Ci	Paper rank(g)2
1	37	37	1
2	35	72	4
3	20	92	9
4	18	110	16
5	17	127	25
6	11	138	36
7 (h-index)	7	145	49
8	7	152	64
9	7	159	81
10	6	165	100
11	5	170	111
12	4	174	144
13(g-index)	4	178	169
14	3	181	196

What is g-index?
The above described disadvantage can be overcome by modifying the h-index a little bit (called g-index) while keeping all advantages of the h-index. The g-index was proposed by Leo Egghe in the year 2006. Using the same list of h-index data table, g-index is defined as the highest rank such that the cumulative sum of the number received is larger than or equal to the square of the rank. The meaning of the g-index can be explained by simple mathematical formula: g2 = S Ci. A researcher (Table 1) has h-index =7 since this is the last rank where all the papers have at least 7 citations. However, he has g-index=13 since this is the last rank for which SCi = g2 (i.e. cumulative sum of citations is equal or greater than g2).

Despite a few limitations, there is now enough evidence to show that the use of the h-index has become popular and acceptable. The h-index is a mathematically single index. It is better index than total number of papers or total number of citations alone. The popularity is well established by the fact that Hirsch’s article has been cited 2325 times (June, 2012) in the Google Scholar and numerous articles related to the h-index are published. To my opinion, h-index itself and consideration of g-index seem to show the most promise for having a long-lasting influence on the field of scientometric indicator.