Theh-index is anauthor-level metric that measures both theproductivity andcitation impact of thepublications, initially used for an individualscientist or scholar. Theh-index correlates with success indicators such as winning theNobel Prize, being accepted for research fellowships and holding positions at top universities.[1] The index is based on the set of the scientist's most cited papers and the number of citations that they have received in other publications. The index has more recently been applied to the productivity and impact of ascholarly journal[2] as well as a group of scientists, such as a department or university or country.[3] The index was suggested in 2005 byJorge E. Hirsch, a physicist atUC San Diego, as a tool for determiningtheoretical physicists' relative quality[4] and is sometimes called theHirsch index orHirsch number.
Hirsch intended theh-index to address the main disadvantages of other bibliometric indicators. The total number of papers metric does not account for the quality of scientific publications. The total number of citations metric, on the other hand, can be heavily affected by participation in a single publication of major influence (for instance, methodological papers proposing successful new techniques, methods or approximations, which can generate a large number of citations). The index works best when comparing scholars working in the same field, since citation conventions differ widely among different fields.[5]
Theh-index is intended to measure simultaneously the quality and quantity of scientific output. TheKendall's correlation ofh-index with scientific awards in physics was found at 34 percent in 2010 and zero percent in 2019.[6]
Theh-index is defined as the maximum value ofh such that the given author/journal has published at leasth papers that have each been cited at leasth times.[4][7]
h-index from a plot of numbers of citations for an author's numbered papers (arranged in decreasing order)
Theh-index is the largesth such thath articles have at leasth citations each. For example, if an author has five publications, with 9, 7, 6, 2, and 1 citations (ordered from greatest to least), then the author'sh-index is 3, because the author has three publications with 3 or more citations. However, the author doesnot have four publications with 4 or more citations.
Clearly, an author'sh-index can only be as great as their number of publications. For example, an author with only one publication can have a maximumh-index of 1 (if their publication has 1 or more citations). On the other hand, an author with many publications, each with only 1 citation, would also have anh-index of 1.
Formally, iff is the function that corresponds to the number of citations for each publication, we compute theh-index as follows: First we order the values off from the largest to the lowest value. Then, we look for the last position in whichf is greater than or equal to theposition (we callh this position). For example, if we have a researcher with 5 publications A, B, C, D, and E with 10, 8, 5, 4, and 3 citations, respectively, theh-index is equal to 4 because the 4th publication has 4 citations and the 5th has only 3. In contrast, if the same publications have 25, 8, 5, 3, and 3 citations, then the index is 3 (i.e. the 3rd position) because the fourth paper has only 3 citations.
f(A)=10,f(B)=8,f(C)=5,f(D)=4,f(E)=3 →h-index=4
f(A)=25,f(B)=8,f(C)=5,f(D)=3,f(E)=3 →h-index=3
If we have the functionf ordered in decreasing order from the largestvalue to the lowest one, we can compute theh-index as follows:
h-index (f) =
The Hirsch index is analogous to theEddington number, an earlier metric used for evaluating cyclists.[8]h-index is also related toSugeno integral andKy Fan metric.[9] Theh-index serves as an alternative to more traditional journalimpact factor metrics in the evaluation of the impact of the work of a particular researcher. Because only the most highly cited articles contribute to theh-index, its determination is a simpler process. Hirsch has demonstrated thath has high predictive value for whether a scientist has won honors likeNational Academy membership or theNobel Prize. Theh-index grows as citations accumulate and thus it depends on the "academic age" of a researcher.
Theh-index can be manually determined by using citation databases or using automatic tools. Subscription-based databases such asScopus and theWeb of Science provide automated calculators. From July 2011Google has provided an automatically calculatedh-index andi10-index within its ownGoogle Scholar profile.[10] In addition, specific databases, such as theINSPIRE-HEP database can automatically calculate theh-index for researchers working inhigh energy physics.
Each database is likely to produce a differenth for the same scholar, because of different coverage.[11] A detailed study showed that the Web of Science has strong coverage of journal publications, but poor coverage of high impact conferences. Scopus has better coverage of conferences, but poor coverage of publications prior to 1996; Google Scholar has the best coverage of conferences and most journals (though not all), but like Scopus has limited coverage of pre-1990 publications.[12] The exclusion of conference proceedings papers is a particular problem for scholars incomputer science, where conference proceedings are considered an important part of the literature.[13] Google Scholar has been criticized for producing "phantom citations", includinggray literature in its citation counts, and failing to follow the rules ofBoolean logic when combining search terms.[14] For example, the Meho and Yang study found that Google Scholar identified 53% more citations than Web of Science and Scopus combined, but noted that because most of the additional citations reported by Google Scholar were from low-impact journals or conference proceedings, they did not significantly alter the relative ranking of the individuals. It has been suggested that in order to deal with the sometimes wide variation inh for a single academic measured across the possible citation databases, one should assume false negatives in the databases are more problematic than false positives and take the maximumh measured for an academic.[15]
Little systematic investigation has been done on how theh-index behaves over different institutions, nations, times and academic fields.[16] Hirsch suggested that, for physicists, a value forh of about 12 might be typical for advancement to tenure (associate professor) at major [US] research universities. A value of about 18 could mean a full professorship, 15–20 could mean a fellowship in theAmerican Physical Society, and 45 or higher could mean membership in theUnited States National Academy of Sciences.[17] Hirsch estimated that after 20 years a "successful scientist" would have anh-index of 20, an "outstanding scientist" would have anh-index of 40, and a "truly unique" individual would have anh-index of 60.[4]
Among the 22 scientific disciplines listed in theEssential Science Indicators citation thresholds (thus excludingnon-science academics), physics has the second most citations afterspace science.[18] During the period between January 1, 2000 and February 28, 2010, a physicist had to receive 2073 citations to be among the most cited 1% of physicists in the world.[18] The threshold for space science is the highest (2236 citations), and physics is followed byclinical medicine (1390) andmolecular biology &genetics (1229). Most disciplines, such as environment/ecology (390), have fewer scientists, fewer papers, and fewer citations.[18] Therefore, these disciplines have lower citation thresholds in the Essential Science Indicators, with the lowest citation thresholds observed in social sciences (154),computer science (149), andmultidisciplinary sciences (147).[18]
Numbers are very different in social science disciplines: TheImpact of the Social Sciences team atLondon School of Economics found that social scientists in the United Kingdom had lower averageh-indices. Theh-indices for ("full") professors, based onGoogle Scholar data ranged from 2.8 (in law), through 3.4 (inpolitical science), 3.7 (insociology), 6.5 (in geography) and 7.6 (in economics). On average across the disciplines, a professor in the social sciences had anh-index about twice that of a lecturer or a senior lecturer, though the difference was the smallest in geography.[19]
There are a number of situations in whichh may provide misleading information about a scientist's output.[20] The correlation betweenh-index and scientific awards dropped significantly since 2010 after the widespread usage ofh-index,[6] followingGoodhart's law. The decrease of correlation is partially attributed to the spread of hyperauthorship with more than 100 coauthors per paper.
Some of the following failures are not exclusive to theh-index but rather shared with otherauthor-level metrics:
Theh-index does not account for the number of authors of a paper. In the original paper, Hirsch suggested partitioning citations among co-authors. One such fractional index is known asfractional h-index, which accounts for multiple authors but is not widely available through the use of automatic tools.[6]
Theh-index does not account for the different typical number of citations in different fields, e.g. experimental over theoretical. Citation behavior in general is affected by field-dependent factors,[21] which may invalidate comparisons not only across disciplines but even within different fields of research of one discipline.[22]
Theh-index discards the information contained in author placement in the authors' list, which in some scientific fields is significant though in others it is not.[23][24]
Theh-index is aninteger, which reduces its discriminatory power.Ruane andTol therefore propose arationalh-index that interpolates betweenh andh + 1.[25]
Theh-index has been found in one study to have slightly less predictiveaccuracy and precision than the simpler measure of mean citations per paper.[26] However, this finding was contradicted by another study by Hirsch.[27] Theh-index does not provide a significantly more accurate measure of impact than the total number of citations for a given scholar. In particular, by modeling the distribution of citations among papers as a randominteger partition and theh-index as theDurfee square of the partition, Yong[28] arrived at the formula, whereN is the total number of citations, which, for mathematics members of the National Academy of Sciences, turns out to provide an accurate (with errors typically within 10–20 percent) approximation ofh-index in most cases.
Weaknesses apply to the purely quantitative calculation of scientific or academic output. Like other metrics that count citations, theh-index can be manipulated bycoercive citation, a practice in which an editor of a journal forces authors to add spurious citations to their own articles before the journal will agree to publish it.[29][30] Theh-index can be manipulated through self-citations,[31][32][33][34] and if based onGoogle Scholar output, then even computer-generated documents can be used for that purpose, e.g. usingSCIgen.[35] Theh-index can be also manipulated byhyperauthorship. Recent research shows clearly that the correlation of theh-index with awards that indicate recognition by the scientific community has substantially declined.[36]
Various proposals to modify theh-index in order to emphasize different features have been made.[37][38][39][40][41][42] Many of these variants, such asg-index, are highly correlated with the originalh-index, which has led some researchers to consider them redundant.[43]
One metric which was found not to be highly correlated withh-index and is correlated with scientific awards as of 2019 is thefractional h-index.[6]
A Hirsch-type index for institutions has also been devised.[44][45] A scientific institution has a successive Hirsch-type index ofi when at leasti researchers from that institution have anh-index of at leasti.
Theh-index has been applied to internet media, such asYouTube channels. It is defined as the number of videosh a channel has with more thanh × 105 views. When compared with a video creator's total view count, theh-index andg-index better capture both productivity and impact in a single metric.[46]
More recently, a dual framework distinguishing betweendisruptive andconsolidating scientific impact has led to the development of new h-index variants.[47]
^Bornmann, Lutz; Daniel, Hans-Dieter (July 2007). "What do we know about the h-index?".Journal of the American Society for Information Science and Technology.58 (9):1381–1385.doi:10.1002/asi.20609.S2CID31323195.
^Jones, T.; Huggett, S.; Kamalski, J. (2011). "Finding a Way Through the Scientific Literature: Indexes and Measures".World Neurosurgery.76 (1–2):36–38.doi:10.1016/j.wneu.2011.01.015.PMID21839937.
Yang, K. (23 December 2006). "A New Era in Citation and Bibliometric Analyses: Web of Science, Scopus, and Google Scholar".arXiv:cs/0612132. (preprint of paper published as 'Impact of data sources on citation counts and rankings of LIS faculty: Web of Science versus Scopus and Google Scholar', inJournal of the American Society for Information Science and Technology, Vol.58, No. 13, 2007, 2105–2125)
^Jacsó, Péter (2006). "Dubious hit counts and cuckoo's eggs".Online Information Review.30 (2):188–193.doi:10.1108/14684520610659201.
^Sanderson, Mark (2008). "Revisitingh measured on UK LIS and IR academics".Journal of the American Society for Information Science and Technology.59 (7):1184–1190.CiteSeerX10.1.1.474.1990.doi:10.1002/asi.20771.
^Turaga, Kiran K.; Gamblin, T. Clark (July 2012). "Measuring the Surgical Academic Output of an Institution: The "Institutional" H-Index".Journal of Surgical Education.69 (4):499–503.doi:10.1016/j.jsurg.2012.02.004.PMID22677589.
^Gálvez, Ramiro H. (March 2017). "Assessing author self-citation as a mechanism of relevant knowledge diffusion".Scientometrics.111 (3):1801–1812.doi:10.1007/s11192-017-2330-1.S2CID6863843.
Kinouchi, Osame; Cardoso, George C. (2018). "The K-index and the hubs of science".European Heart Journal.39 (38):3489–3490.doi:10.1093/eurheartj/ehy613.PMID30295763.
^Bornmann, L.; et al. (2011). "A multilevel meta-analysis of studies reporting correlations between theh-index and 37 differenth-index variants".Journal of Informetrics.5 (3):346–359.doi:10.1016/j.joi.2011.01.006.
^Kosmulski, M. (2006). "I – a bibliometric index".Forum Akademickie.11: 31.
^Prathap, G. (2006). "Hirsch-type indices for ranking institutions' scientific research output".Current Science.91 (11): 1439.
^Hovden, R. (2013). "Bibliometrics for Internet media: Applying theh-index to YouTube".Journal of the American Society for Information Science and Technology.64 (11):2326–2331.arXiv:1303.0766.doi:10.1002/asi.22936.S2CID38708903.
^Yang, Alex J.; et al. (2023). "From consolidation to disruption: A novel way to measure the impact of scientists and identify laureates".Information Processing & Management.60 (5) 103420.doi:10.1016/j.ipm.2023.103420.
Kelly, C. D.; Jennions, M. D. (2006). "Theh index and career assessment by numbers".Trends in Ecology & Evolution.21 (4):167–170.doi:10.1016/j.tree.2006.01.005.PMID16701079.
