The h-index is an author-level metric that measures both the productivity and citation impact of the publications, initially used for an individual scientist or scholar. The h-index correlates with success indicators such as winning the Nobel Prize, being accepted for research fellowships and holding positions at top universities. 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 a scholarly journal as well as a group of scientists, such as a department or university or country. The index was suggested in 2005 by Jorge E. Hirsch, a physicist at UC San Diego, as a tool for determining theoretical physicists' relative quality and is sometimes called the Hirsch index or Hirsch number. Hirsch intended the h-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. The h-index is intended to measure simultaneously the quality and quantity of scientific output. The Kendall's correlation of h-index with scientific awards in physics was found at 34 percent in 2010 and zero percent in 2019.
Calculation The h-index is defined as the maximum value of h such that the given author/journal has published at least h papers that have each been cited at least h times.
The h-index is the largest h such that h articles have at least h 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's h-index is 3, because the author has three publications with 3 or more citations. However, the author does not have four publications with 4 or more citations. Accordingly, an author's h-index can only be as great as their number of publications. For example, an author with only one publication can have a maximum h-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 an h-index of 1. Formally, if f is the function that corresponds to the number of citations for each publication, we compute the h-index as follows: First we order the values of f from the largest to the lowest value. Then, we look for the last position in which f is greater than or equal to the position (we call h 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, the h-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 function f ordered in decreasing order from the largest value to the lowest one, we can compute the h-index as follows:
h-index (f) = max { i ∈ N : f ( i ) ≥ i } {\displaystyle \max\{i\in \mathbb {N} :f(i)\geq i\}}
The Hirsch index is analogous to the Eddington number, an earlier metric used for evaluating cyclists. h-index is also related to Sugeno integral and Ky Fan metric. The h-index serves as an alternative to more traditional journal impact factor metrics in the evaluation of the impact of the work of a particular researcher. Because only the most highly cited articles contribute to the h-index, its determination is a simpler process. Hirsch has demonstrated that h has high predictive value for whether a scientist has won honors like National Academy membership or the Nobel Prize. The h-index grows as citations accumulate and thus it depends on the "academic age" of a researcher.
Input data The h-index can be manually determined by using citation databases or using automatic tools. Subscription-based databases such as Scopus and the Web of Science provide automated calculators. From July 2011 Google has provided an automatically calculated h-index and i10-index within its own Google Scholar profile. In addition, specific databases, such as the INSPIRE-HEP database can automatically calculate the h-index for researchers working in high energy physics. Each database is likely to produce a different h for the same scholar, because of different coverage. 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. The exclusion of conference proceedings papers is a particular problem for scholars in computer science, where conference proceedings are considered an important part of the literature. Google Scholar has been criticized for producing "phantom citations", including gray literature in its citation counts, and failing to follow the rules of Boolean logic when combining search terms. 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 in h 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 maximum h measured for an academic.
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