G-index

Last updated November 12, 2024

The g-index is an author-level metric suggested in 2006 by Leo Egghe.^[1] The index is calculated based on the distribution of citations received by a given researcher's publications, such that given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the unique largest number such that the top g articles received together at least g² citations. Hence, a g-index of 10 indicates that the top 10 publications of an author have been cited at least 100 times (10²), a g-index of 20 indicates that the top 20 publications of an author have been cited 400 times (20²).

It can be equivalently defined as the largest number n of highly cited articles for which the average number of citations is at least n. This is in fact a rewriting of the definition

An example of a g-index (the raw citation data, plotted with stars, allows the h-index to also be extracted for comparison). Gindex1.jpg — An example of a g-index (the raw citation data, plotted with stars, allows the h-index to also be extracted for comparison).

g^{2}\leq \sum _{i\leq g}c_{i}

as

g\leq {\frac {1}{g}}\sum _{i\leq g}c_{i}.

The g-index is an alternative for the older h-index. The h-index does not average the number of citations. Instead, the h-index only requires a minimum of n citations for the least-cited article in the set and thus ignores the citation count of very highly cited publications. Roughly, the effect is that h is the number of works of a quality threshold that rises as h rises; g allows citations from higher-cited works to be used to bolster lower-cited works in meeting this threshold. In effect, the g-index is the maximum reachable value of the h-index if a fixed number of citations can be distributed freely over a fixed number of publications. Therefore, in all cases g is at least h, and is in most cases higher.^[1] The g-index often separates authors based on citations to a greater extent compared to the h-index. However, unlike the h-index, the g-index saturates whenever the average number of citations for all publications exceeds the total number of publications; the way it is defined, the g-index is not adapted to this situation. However, if an author with a saturated g-index publishes more, their g-index will increase.

An example of two authors who both have 10 publications, both authors have a h-index of 6. However, Author 1 has a g-index of 10, while Author 2 has a g-index of 7.
	Author 1	Author 2
Work 1	30	10
Work 2	17	9
Work 3	15	9
Work 4	13	9
Work 5	8	8
Work 6	6	6
Work 7	5	5
Work 8	4	4
Work 9	3	2
Work 10	1	1
Total cites	102	63
Average cites	10,2	6,3

The g-index has been characterized in terms of three natural axioms by Woeginger (2008).^[2] The simplest of these three axioms states that by moving citations from weaker articles to stronger articles, one's research index should not decrease. Like the h-index, the g-index is a natural number and thus lacks in discriminatory power. Therefore, Tol (2008) proposed a rational generalisation.^[3]^{[ clarification needed ]}

Tol also proposed a collective g-index.

Given a set of researchers ranked in decreasing order of their g-index, the g₁-index is the (unique) largest number such that the top g₁ researchers have on average at least a g-index of g₁.

Related Research Articles

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation $on some set, which satisfies the following for all and in :$

$(reflexive).$
If $and then (transitive).$
If $and then (antisymmetric).$
$or .$

In mathematics, a monotonic function is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.

A citation is a reference to a source. More precisely, a citation is an abbreviated alphanumeric expression embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work for the purpose of acknowledging the relevance of the works of others to the topic of discussion at the spot where the citation appears.

In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical structure that satisfies the definition.

The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as indexed by Clarivate's Web of Science.

Scientometrics is a subfield of informetrics that studies quantitative aspects of scholarly literature. Major research issues include the measurement of the impact of research papers and academic journals, the understanding of scientific citations, and the use of such measurements in policy and management contexts. In practice there is a significant overlap between scientometrics and other scientific fields such as information systems, information science, science of science policy, sociology of science, and metascience. Critics have argued that overreliance on scientometrics has created a system of perverse incentives, producing a publish or perish environment that leads to low-quality research.

Citation analysis is the examination of the frequency, patterns, and graphs of citations in documents. It uses the directed graph of citations — links from one document to another document — to reveal properties of the documents. A typical aim would be to identify the most important documents in a collection. A classic example is that of the citations between academic articles and books. For another example, judges of law support their judgements by referring back to judgements made in earlier cases. An additional example is provided by patents which contain prior art, citation of earlier patents relevant to the current claim. The digitization of patent data and increasing computing power have led to a community of practice that uses these citation data to measure innovation attributes, trace knowledge flows, and map innovation networks.

Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses and dissertations, preprints, abstracts, technical reports, and other scholarly literature, including court opinions and patents.

Informetrics is the study of quantitative aspects of information, it is an extension and evolution of traditional bibliometrics and scientometrics. Informetrics uses bibliometrics and scientometrics methods to study mainly the problems of literature information management and evaluation of science and technology. Informetrics is an independent discipline that uses quantitative methods from mathematics and statistics to study the process, phenomena, and law of informetrics. Informetrics has gained more attention as it is a common scientific method for academic evaluation, research hotspots in discipline, and trend analysis.

"Publish or perish" is an aphorism describing the pressure to publish academic work in order to succeed in an academic career. Such institutional pressure is generally strongest at research universities. Some researchers have identified the publish or perish environment as a contributing factor to the replication crisis.

Citation impact or citation rate is a measure of how many times an academic journal article or book or author is cited by other articles, books or authors. Citation counts are interpreted as measures of the impact or influence of academic work and have given rise to the field of bibliometrics or scientometrics, specializing in the study of patterns of academic impact through citation analysis. The importance of journals can be measured by the average citation rate, the ratio of number of citations to number articles published within a given time period and in a given index, such as the journal impact factor or the citescore. It is used by academic institutions in decisions about academic tenure, promotion and hiring, and hence also used by authors in deciding which journal to publish in. Citation-like measures are also used in other fields that do ranking, such as Google's PageRank algorithm, software metrics, college and university rankings, and business performance indicators.

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.

In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory.

Journal ranking is widely used in academic circles in the evaluation of an academic journal's impact and quality. Journal rankings are intended to reflect the place of a journal within its field, the relative difficulty of being published in that journal, and the prestige associated with it. They have been introduced as official research evaluation tools in several countries.

Academic authorship of journal articles, books, and other original works is a means by which academics communicate the results of their scholarly work, establish priority for their discoveries, and build their reputation among their peers. Through authorship, researchers, assistants, interns, students, and other involved parties receive credit for their contributions and can be held responsible and accountable for the quality and integrity of the work.

<i>Journal of Forestry</i> Academic journal

The Journal of Forestry is the primary scholarly journal of the Society of American Foresters. It aims to advance the forestry profession by keeping professional foresters informed about developments and ideas related to the practice of forestry. The journal publishes editorials and technical content related to the management of forests and related natural resources. Articles are generally written for an audience of natural resources professionals, with topics spanning the many facets or disciplines of forestry. The Journal is currently edited by Keith A. Blatner. According to the Journal Citation Reports, its 2018 impact factor is 2.675.

In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.

Author-level metrics are citation metrics that measure the bibliometric impact of individual authors, researchers, academics, and scholars. Many metrics have been developed that take into account varying numbers of factors.

Ronald Rousseau is a Belgian mathematician and information scientist. He has obtained an international reputation for his research on indicators and citation analysis in the fields of bibliometrics and scientometrics.

The science-wide author databases of standardized citation indicators is a multidimensional ranking of the world's scientists produced since 2015 by a team of researchers led by John P. A. Ioannidis at Stanford.

References

1 2 Egghe, Leo (2006). "Theory and practise of the g-index". Scientometrics. 69 (1): 131–152. doi:10.1007/s11192-006-0144-7. hdl: 1942/981 . S2CID 207236267.
↑ Woeginger, Gerhard J. (2008). "An axiomatic analysis of Egghe's g-index". Journal of Informetrics. 2 (4): 364–368. doi:10.1016/j.joi.2008.05.002.
↑ Tol, Richard S. J. (2008). "A rational, successive g-index applied to economics departments in Ireland". Journal of Informetrics. 2 (2): 149–155. doi:10.1016/j.joi.2008.01.001. Preprint.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Egghe-1] 1 2 Egghe, Leo (2006). "Theory and practise of the g-index". Scientometrics. 69 (1): 131–152. doi:10.1007/s11192-006-0144-7. hdl: 1942/981 . S2CID 207236267.

[2] Woeginger, Gerhard J. (2008). "An axiomatic analysis of Egghe's g-index". Journal of Informetrics. 2 (4): 364–368. doi:10.1016/j.joi.2008.05.002.

[3] Tol, Richard S. J. (2008). "A rational, successive g-index applied to economics departments in Ireland". Journal of Informetrics. 2 (2): 149–155. doi:10.1016/j.joi.2008.01.001. Preprint.

[1]

[2]

[3]