The h-index

The h-index is a mainstream bibliometric indicator, since it is widely used in academia, research management and research policy. While its advantages have been highlighted, such as its simple calculation, it has also received widespread criticism. The criticism is mainly based on the negative effects it may have on scholars, when the index is used to describe the quality of a scholar. The"h"means"highly-cited"and"high achievement", and should not be confused with the last name of its inventor, Hirsch. Put simply, the h-index combines a measure of quantity and impact in a single indicator. Several initiatives try to provide alternatives to the h-index to counter some of its shortcomings.


Introduction
The h-index wasdevelopedbyJorge Hirsch, aphysicist at the University of California at San Diego, who published the concept in the Proceedings of the National Academy of Sciences of the USA (Hirsch, 2005). The h-index was defined by Hirsch as follows: "Ascientist has index h if h of his or her N p papers have at least h citations each and the other (N p -h)p apers have ≤ h citations each." (Hirsch, 2005) The "h" means "highly-cited" and "higha chievement",a nd should not be confused with the last name of its inventor (Hirscha nd Buela-Casal, 2014; Schuberta nd Schubert,2 019). Put simply,the h-index "combines am easure of quantity and impact in as ingle indicator" (Costas and Bordons, 2007).
While the h-index was proposed in 2005 and is considered aclassicalbibliometric indicator,there is still an ongoing debate on its value in bibliometrics and in the scholarlyc ommunity in general. Due to its popularity,i th as even been called a mainstream bibliometric indicator (Costas and Franssen, 2018). It is one of the most well-known indicators,b ut it has receivedn egative and positive judgements alike.
The developmentofindicators was part of ashift from higher level entities (e. g., countries,i nstitutions, journals) towards the bibliometrics of individual researchers (Costas, vanLeeuwen, and Bordons,2010;Hicks et al., 2015). This shift was related to how single researchers' research outputs should be measured via quantitative indicators.H ow analyses should be conducted on an individual level was and still remains an open question in bibliometrics (Bornmanna nd Marx,2014). The relatively simple h-index calculation has contributed to its widespread use (Sugimoto and Larivière, 2018), and it waspromoted in several journals and news outletsinthe beginning (Ball, 2005). Hirsch'soriginal work from 2005,for example, has been cited 4,530 times accordingt ot he bibliographic databases Scopus (accessed October 25,2 019), 3,999 times accordingt oWebo fS cience (accessed October 25,2 019) and 5,240 times according to TheLens (accessed September 23,2019). Due to the high number of publications on the h-index (Waltman, 2016), this book chapter focuses on some central topics of h-index research and refers mostlyt oc omprehensive literature reviews (Costas and Bordons,2 007).

h-index History
The quantitative distribution of scholarlyw orks on the h-index over ap eriod of 13 years mayprovide an insight into its historicaldevelopment.Therefore, abibliometric analysis was conducted based on the bibliographic database TheL ens (Jefferson et al., 2018) to query all works for "h-index" in the title, abstract,keywordorfield of study. All publicationsf rom  The h-index has been applied in several academic disciplines, such as physics, biomedicine, informations cience and business studies (Costas and Bordons, 2007). However,acomparison between disciplines by using the h-index is not recommended (Hirsch, 2005;van Leeuwen, 2008) because of different citation practices,among others. There are attempts to put the h-index in ac ommon scale in order to make inter-field comparisons possible (Iglesias and Pecharromán, 2007).
Due to the ever increasing number of online sources thatp rovide bibliometric data, the possibilityt oc alculate and/or displayt he h-index has also changed dramatically ( Costas and Franssen, 2018;T eixeirad aS ilva and Dobránszki, 2018). For example, the h-index is prominentlyp laced on Google Scholar profiles (Costas and Wouters,2012;Sugimoto and Larivière, 2018) and alsointhe WebofScience and Scopus (Leydesdorff, Bornmann, and Opthof, 2019).
The scope of application of the h-index has been extended, for instance, to journals (e. g., Braun, Glänzel, and Schubert,2 006) and to research groups (e. g., van Raan, 2006). Several variants of the h-index have been developedtoaddress specific limitations of the h-index (seesection 4), for example, the g-index as the most prominent one (Egghe, 2006).

h-index Concept
In order to enhance the understanding of the basic h-index concept,agraphicalderivation of the index could be helpful (Alonso et al., 2009). In Figure 2t he so-called rank frequency distribution for ar esearcher is shown.H is or her publications are sorted in descendingo rder accordingt ot heir citations.T he publicationw ith the highestcitation is ranked first,then the publication with the second highest citation and so on. The h-index corresponds to intersection between the rank-frequencyd istribution and the 45°degree line, wherethe number of papers is equal to the number of publications. Fort he specific researcher the h-index amounts to 22.T he h-core comprises 22 publications, which contribute to the h-index and are cited at least 22 times. Neither the number of citations the highlycited papers receive nor the papers outside the h-corea re of importance.
Several advantagesofthe h-index were discussed in the literature (Alonso et al., 2009;B ornmanna nd Daniel, 2005;B ornmann and Daniel, 2007;C ostas and Bordons, 2007). It is ar obust indicator in the sense that it is rather insensitive to lowlycited papers.I tisanobjectiveindicatora nd might playacertain role together with other indicators and expert judgementsduringfunding or promotion decisions. It claims to perform better than anys ingle indicator.H irsch himself postulatedt hat the h-index has apredictive capacity for researchers' careers to agreater extent than conventional citation indicators (Alonso et al., 2009;H irsch, 2007). Bornmanna nd Daniel (2005), for instance, found that the h-index for successful applicants for post-doctoral biomedicine fellowships was significantlyhigher thanfor non-successful applicants.

h-index Problemsa nd Alternatives
The h-index is widelyused by researchers,for example in the medical sciences(Cronin and Sugimoto, 2014), but it has also been widelycriticised (Bornmann, Mutz, and Daniel, 2010;H auschke, 2019;W altman and van Eck, 2012). The h-index'sw idespread availability online has the potential for problematic usagei nr esearch evaluation, which should never rely on asingle indicator (Costas and Bordons,2007). Conversely, this simplicity and objectivity is sometimes also seen as an advantage of the h-index (Alonso et al., 2009). However,the indicator could alsolead to questionable self-citation practicescarried out to increase the h-index (Costas and Bordons,2007). Fore xample, the h-index mayb ep roblematic due to the Matthew effect,whereby a high-profile researcher mayattract more and more citations based on her or his displayed h-index (Alonso et al., 2009).
Costas and Bordons pointed out the problem of size dependency of the h-index. Imagine the following scenario: [S]cientist "A" with 10 documents cited 10 times each would have an h-index of 10;whereas scientist "B",with 5documents which were cited 200times each, would onlyachieveanh-index of 5. Scientist "B" publishes fewer documents,b ut their impact is much higher than the other's (i. e., ahigher citation per document rate).Scientist "A" publishes manymoredocuments,albeit with al ower impact.D espitet his, according to the h-index, scientist Aw ould be regarded as much mores uccessfult han "B" (Costas and Bordons,2 007). The example aboveillustratesthat researchers with ahigher h-index might be those who have ah ighq uantity of publications with averagec itations compared to researchers thatp ublish less but have af ew highly-cited publications (Costas and Franssen, 2018).
The h-index is alsoi nfluenced by the length of ar esearcher'sc areer or lifetime citedness (Alonso et al., 2009;Ball, 2017;Bornmann and Marx, 2011;Costas and Bordons, 2007;Hicks et al., 2015). It combines quantity as well as impact in one indicator or single number (Hirsch, 2005). Colloquially,this concept might alsobecalled an all-in-one metric (Bornmann and Marx, 2011), while its value cannot decrease because it relies on the number of publications and citations (Gingras, 2016). Obviously,this focus on lifetime citedness maybed isadvantageous to earlycareer researchers. The mergero ft wo concepts in one indicator has alsob een criticised (Sugimoto and Larivière, 2018), even if Hirsch'so riginal proposal was to simplify "to [a] great extent the characterization of researchers' scientific output" (Alonso et al., 2009). Furthermore, the h-index might be manipulated, for example in Google Scholar (Costas and Wouters,2012;Gingras, 2016). Additionally, it does not distinguish between negative or positive citations (Alonso et al., 2009), although such adistinctionisdifficult to achieveasitrequires naturallanguageprocessing (Teufel,Siddharthan,and Tidhar,2 006). Ar esearcher could have ad ifferent h-index depending on the bibliographic database (Bar-Ilan, 2008;Hicks et al., 2015) and academic disciplines (Hicks et al., 2015). Lists of researchers thatdisplaytheir h-index¹ maybeinsightful, but the use of the h-index in hiring and promotion decisionsmight be problematic (Hicks et al., 2015). According to the Leiden Manifesto (Hicks et al., 2015,Principle 7), the San Francsico Declaration on Research Assessment (DORA) ( Cagan, 2013,P rinciple 3), and the HongK ong Principles( Moher et al., 2020,P rinciple 1), research assessment of individual researcher should consider abroad rangeofbibliometric measures,not onlyasingle indicator, such as the h-index. In general, quantitative research assessment should support not replacequalitative judgements of experts(e. g., peer review) (Hicks et al., 2015).
Alternative types of indicators have been studied, such as the g-index (Costas and Bordons,2008;Egghe, 2006), the hg-index, the A-index, and the m-index (Alonso et al., 2009). Meta-analyses have been carried out to studyc orrelations between the h-index and its variants (Bornmann et al., 2011), such as the g-index. Strikingly, a2011 meta-analysis concluded that 35 out of 37 variants seemed to duplicatethe hindex,e xceptf or the modified impact index (MII)a nd m-index (Bornmann et al., 2011). This meanst hat most variants are highlyc orrelated with the h-index (Bornmann and Mutz et al., 2009). Bornmann et al. alsoc ategorised the variants into two groups,namely the "impact of the productive core" and the "quantity of the productive core".The productive corer efers to the most receivedc itations (Bornmann, Mutz, and Daniel, 2008). Studies have also concluded that the h-index and its var- https://www.webometrics.info/en/hlargerthan100 (July1 5, 2020).

The h-index
iants are not needed compared to standard bibliometric measures,s uch as number of publications and total citation counts (Bornmann,Mutz, and Daniel, 2009). Due to these findings,s ome scholars suggested not developing new variants of the h-index anylonger (Bornmann and Marx et al., 2009) but rather to complement or enrich the h-index with additional information (Bornmann, Mutz, and Daniel, 2010). Variantsof the h-index, such as the ones mentioned above, are alsor egarded as superficial enhancements (Waltman, 2016). From abibliometric perspective,the h-index seems to have no analyticalvalue as such (Leydesdorff, Bornmann, and Opthof, 2019), despite its frequent use in academia,research management and policy.Initiativesare underwayt oe mploy indicators by involvingt he scholarlyc ommunity (Hauschke,Cartellieri,and Heller,2 018), to overcome the evaluation gapb etween what is measured by indicators and what is valued by researchers (Heuritsch, 2018;W outers,2 017).

Conclusions
This article has provided an overviewo ft he h-index, described its applications, reviewed several studies that scrutiniset he h-index and discussed its advantagesa nd disadvantages. Developed by Hirsch in 2005 as an "index to quantify an individual's scientifico utput" (Hirsch, 2005), the h-index is still being debated almost1 5y ears later.Avast amount of literature on the h-index is available. As such, it is perhaps one of the most studied topics in bibliometrics and scientometrics, and it has had an influenceo nt he scholarlyc ommunity as aw hole and even beyond on research management and policy.S everal variants of the h-index have been developed over the years, but asignificant improvement would be to provide additional information and indicators and explain the h-index context.The h-index certainlyalso has some advantages, such as its simple calculation and wide availability.Aproblem that remains is its isolated use in research evaluation, potential comparisons among academic disciplines and the fact thatitistaken by some at face value to judge the quality of ar esearcher'sw ork. Finally, the displayo ft he h-index in bibliographic databases,s uch as Google Scholar,c odifiest his indicator (Sugimoto and Larivière, 2018) and normalises its perception. The future of the h-index is stillbeing debated, but the negative assessments seem to be in the majority.