Bibliometrics is described as ‘the use of mathematical and statistical methods to books and other forms of communication’ by Pritchard, A. (1969) (Velmurugan and Radhakrishnan 2016). The bibliometrics literature suggests that “quality” is quantitatively unattainable, as the academic value of a publication remains indeterminate until its impact on subsequent literature can be assessed, despite the frequent citation of the number of peer-reviewed articles as a metric of research quality (Donovan, 2007). Bibliometric methods are employed to analyze authorship, citation and publication patterns, as well as the interrelationships within scientific domains, research communities, and the structure of specific fields (Vijay and Raghavan 2007; Jermann et al., 2015; Verma et al., 2015; Demir and Sharma, 2020). The examination of documents utilizing diverse statistical methodologies can guide investigative studies, characteristics, and behaviors of published knowledge, facilitating the exploration of research structures and scientific domains, as well as the evaluation of scientific information management and research activities (Velmurugan and Radhakrishnan 2016).

A paper with a high citation count is more likely to garner further citations compared to one with a low count. An author with several publications is more likely to republish than one with fewer works (Price, 1976). Numerous methodologies exist for assessing the cumulative influence and significance of scientific research outputs from academics outside a select few Nobel Prize laureates, whose research impact and relevance are indisputable (Hirsch 2005a). It has recently assumed a crucial position in the assessment and evaluation of research performance. The Hirsch index, or h, assesses the weight, relevance, and overall impact of a scientist’s cumulative research contributions. When scientific achievement is a primary evaluation criterion, the h-index may provide a useful standard for objectively evaluating several applicants competing for the same resource (Hirsch 2005a). Furthermore, the h-index exhibits robustness as it stays impervious to a cluster of uncited or inadequately cited works, as well as to a limited number of highly cited articles, and it does not account for numerous co-authorships. The hm-index, an alternative to the h-index, quantifies articles fractionally according to numerous co-authorships. The hm is calculated in a manner akin to the h index, by dividing the total number of authors by the total number of citations for each work (Schreiber, 2008). The g-index inherits all the favorable characteristics of the h-index while additionally providing a more precise evaluation of the citation counts of the most highly rated articles (Egghe, 2006). Variations of the h index, including the m quotient (Hirsch, 2005b), g index (Egghe, 2006), h (2) index (Kosmulski, 2006), A index (Jin, 2006), R index (BiHui et al., 2007), AR index (BiHui et al., 2007), hw index (Egghe and Rousseau, in press), and b index (Bornmann et al., 2007), have been proposed to address its limitations.

The analysis of citations in scholarly literature, referred to as scientometrics or informetrics, considers the increase in publications, journals, and researchers. Mingers and Leydesdorff (2015) examine the historical progression of scientometrics, sources of citation data, citation metrics and their “laws,” normalization, journal impact factors and other journal metrics, the mapping and visualization of research, evaluation and policy, as well as future advancements. Mingers and Leydesdorff (2015); Nalimov and Mulchenko (1971).

Ioannidis et al., (2016) analyzed all scientists ranked within the top 30,000 (0.28%) based on six principal metrics: number of citations (nc), citations for which the scientist is the sole author (ns), citations for which the scientist is either the sole or first author (nsf), citations for which the scientist is the sole, first, or last author (nsfl), Hirsch index (h), and Schreiber co-authorship adjusted index (hm). The 2023 list of Stanford scientists was examined, resulting in the selection of researchers from India. In 2023, the Stanford dataset metrics identified 217,097 scientists based on comprehensive career variables from 166 countries. This study analyzes the bibliometric attributes and characteristics of the Stanford scientist list for 2,939 researchers based in India. This study is significant for offering a comprehensive overview of the progress of Indian scientists, whose 50 universities rank among the top 1200 globally, and whose substantial contributions to science are evident in their global diaspora, as well as the advancement of Indian scientists nationally over the years. A bibliometric analysis of Indian scientists was performed, focusing on year, subfield category, author rank, citation index, affiliated universities, six key indicators for career-long and single-year performance, and the overall distribution of authors in the Stanford list, illustrated in a heat map utilizing Bibliometrix (Aria and Cuccurullo, 2017) and MS Excel.

David Pendlebury said that “Research fuels the race for knowledge and it is important that nations and institutions celebrate the individuals who drive the wheel of innovation” (Web3, 2023). Meanwhile, the percentage of collaboration by many researchers is rising, thus it’s critical to take their respective contributions into consideration. In the literature, multiple performance indicators are used in science and scientific evaluation which are citation analysis (citation impact of authors, articles, and journals), h-index/ g-index (quantify the impact of an individual author), hm-index (co-authorship adjustment), i10-index (number of publications at least 10 times), use/download data (number of downloads for article), journal of impact factor (average citation count for a journal), and scientometrics 2.0/altmetrics (measurement of scholarly impact) etc. (Priem et al., 2010). Multiple citation indicators, including overall impact, co-authorship adjustment, and author order (specifically, single, first, or last position authorships, since these positions reflect crucial contributions to the work) were investigated by the Stanford database metrics.

Ioannidis et al., (2016) used the Scopus database in the Meta-Research Innovation Center at Stanford (METRICS). They performed such an evaluation of 84,116 influential scientists across 12 scientific fields (physics, mathematics, computer science, chemistry, earth sciences, engineering, biology/biotechnology, infectious disease, medicine, brain research, health sciences, social sciences).

The updated science-wide author databases of standardized citation indicators tables were downloaded for 2017 and 2018 (Ioannidis, 2019), 2019 (Baas et al., 2020), 2020 (Baas et al., 2021), 2021 (Ioannidis 2022), 2022 (Ioannidis 2023) and 2023 (Ioannidis 2024). In this study, the search was made in February 2025. All these data were organized, analyzed, tabulated, and presented by using simple statistical methods in MS excel. The data set tables covered for the career of scientists that were initiated prior to 1996 and for single year. The dataset tables involve six key indicators which are determined and/or analyzed for excluded self-citation for all authors contributed to article and total citations. Ioannidis et al., (2016) calculated the c (composite) indicator, any scientist may use the following equation composed of six key indicators.

The variables value depends on whether the indicator c is calculated by career or single year. Moreover, the indicator c was calculated for excluding self-citation for all authors contributed to the article and total citations. Where nc is the total number of citations, h is the h-index, hm is the Schreiber co-authorship-adjusted index, ncs is the number of citations to single-author articles, ncsf is the number of citations to single or first-author articles, and ncsfl is the number of citations to single, first, or last author articles. The maximum values, nc_max, h_max, hm_max, ncs_max, ncsf_max, and ncsfl_max were found for career, single year, excluded self-citation or total citations individually. Ioannidis et al., (2016) were described 176 category names such as Agronomy and Agriculture, Dairy and Animal Science, Biotechnology etc.

Figure 1 illustrates the top 25 countries for the number of scientists listed in Stanford dataset metrics according to career long metrics. The Stanford dataset metrics in 2017 and 2023 listed 105026 and 217097 scientists according to career long metrics, respectively. The 84202 scientists from the United States are listed in the Stanford dataset metrics. The percentage with a US scientist was 38.8% in 2023. India has 2939 scientists, placing it 13^th in the Stanford dataset metrics according to career long metrics. The first five countries’ percentage of scientists was 57.1%. The countries, the number of scientists indexed on the Stanford list increased by an average of 3-fold from 2017 to 2023. From 2017 to 2023, the number of scientists indexed on the Stanford list rose by an average of three times across the nations.

Figure 1:
Top 25 countries for number of scientists listed in Stanford dataset metrics for career long period.

Figure 2 depicts the year-wise number of scientists listed in Stanford dataset metrics according to the single year and career of the scientists. The Stanford dataset shows a consistent yearly growth in the number of listed. The maximum number of scientists listed in the Stanford dataset was observed in Figure 2 as 5351 in 2023 according to single year metrics. The number of listed authors will rise because of the citation indexing databases’ recent progress, which has decreased the confusion caused by name similarities while recognizing scientists and classifying their publications. This is a significant issue for scientists, particularly in nations like India where there is a large population density and a high degree of name similarity.

Figure 2:
Year-wise number of scientists listed in Stanford dataset metrics.

Table 1 reveals year wise world-wide percentage of Indian author and threshold of six key indicators which are the total number of citations, h index, Schreiber co-authorship adjusted index, the number of citations to single-author articles, the number of citations to single or first-author articles, the number of citations to single, first, or last author articles and composite score for career-long and single year. Ioannidis et al., (2016) assessed the composite score, which combines the standardized values of these six log-transformed indicators. In 2022, overall average composite scores were 2.7529 and 3.4739 for single year and career long metrics, respectively. In 2023, overall average composite scores were 2.7152 and 3.4584 for single year and career long metrics, respectively. The c scores of Indian scientists for both career and single years perspective were very close to overall average values. In 2022 and 2023, overall average h-index were approximately 12.3 and 40.0 for single year and career long metrics, respectively. The h-index of Indian scientists were also close to overall average values for both career and single year perspective. The average total number of citations for 2022 were 971 and 8813 for single year and career long metrics, respectively. For 2023, The average total number of citations were reported as 958 and 9349 for single year and career long metrics, respectively. The share of year wise Indian scientists in Stanford dataset was observed continuous and steadily increment. The Indian scientists’ percentages reached in 2023 as 1.35 and 2.40 for single year and career long metrics, respectively. The composite score which is calculated and used in the Stanford dataset metrics evaluates a more successful ranking than evaluating according to total citations. The citation of an article depends on many different parameters and factors. In some cases, it would be more accurate to attribute citations to the success of the article rather than to an author. According to Ioannidis et al., (2016), many of the top 1,000 authors in terms of overall citations do not have a single or last-authored cited work. As a result, while citations constitute a significant element in a scientific index, they are not the only index criterion.

Scopus was divided into 12 categories for indexed published items which are physics, mathematics, computer science, chemistry, earth sciences, engineering, biology/biotechnology, infectious disease, medicine, brain research, health sciences, social sciences (Börner et al., 2012). Ioannidis et al., (2019) investigated 6,880,389 scientists and his/her research field in the career-long data from 1996-2017. Ioannidis et al., (2016) and Ioannidis et al., (2019) classified and/or defined the scientists research fields in 22 fields and 176 subfields as well. Figure 3 shows top 20 subfield category which are the most popular around the Indian scientists. Mechanical engineering and transports, applied physics, artificial intelligence and image processing, energy, and materials are most studied fields more than 100 Indian scientist in 2023 as it seen in Figure 3. It is not surprising that the most popular research areas that have gained importance in recent years; materials, energy and artificial intelligence are widely studied by Indian scientists.

Figure 3:
The number of scientists for the top 20 subfield category.

Table 2 reveals top 100 Indian scientists which were ranked according to composite score in the Stanford dataset metrics. As is seen in the table, some rankings were missed in some case last scores some cases first scores were not written. These problems may become because of name-surname similarities. Citation databases still need to be improved themselves, i.e. databases must develop author recognition and/or name similarity sorting systems. It causes confusion when databases assign distinct ID numbers to an author. Although the confusion is not obvious since databases do their own searches, having too many ID numbers for one author limits traceability. Accepting disparate databases’ ORCID (Open Researcher and Contributor Identifier) numbers as an author ID enables database comparison and/or information merging while also being unaffected by name changes, cultural differences in name order, inconsistent abbreviations, or the use of different alphabets. The gender of top 100 scientists was analyzed that 6 of top 100 scientists are women. The top 100 scientists are 20% of chemists, 18% of physicists, 21% of clinical medical, and 14.5% of artificial intelligence.

Table 3 presents the single year total number of citations excluding self-citation for the last three years. As was already noted, the most common statistic for evaluating the influence (or lack thereof) of a journal article is its citation count. However, this should not be the only method used to determine impact. Before evaluation of an article based on a citation, the following limitations of citations should be considered (web1, 2024):

• Cited positively/negatively: An article may be heavily quoted because it is contentious, satirical, or its assertions are being contested.
• Types of articles: Review papers tend to be more well-cited than original research papers
• Prestige effect: to cite a well-known paper over a lesser-known paper is possible.
• Languages: preventing readers from finding and citing non-English research.

Table 3 shows the top ten scientists who have been consistently highly cited in the last three years. Almost all scientists cited more than 10,000 citations every year. Despite various limitations and controversies, receiving such a high number of citations per year is a significant achievement. The number of papers and citations per paper are inversely related to each other. Having a high number of articles and citations per article does not mean that the rank of the scientist is better. Because the number of articles and citations per article values of 84,116 scientists listed in Stanford database metrics are quite different, the number of papers varied from 1 to 2,533, and citations per paper varied from 0.08 to 5318 (Ioannidis et al., 2019).

Table 4 depicts year wise self-citation percentage for career-long and single year. Self-citation occurs in an article when an author refers to one of their own publications. This can be a respectable approach to refer to previous discoveries, but self-citations can also be used to artificially raise an individual’s citation count (web 1, 2024). When analyzing the performance of scientists, it is necessary to exclude the number of self-citations. Available citation databases have the option of extracting authors’ self-citations. Ioannidis et al., 2019 reported that the median was 3.3% and the mean was 5.5% among the 84,116 scientists. According to this information the self-citation percentages seemed to be higher.

Figure 4 shows the number of ranked scientists involved in the top 25 Universities and Times Higher Education (THE) Indian university rankings. 11 universities and or institutions were not ranked in THE world university rankings table. Interestingly, the top 4 universities having the maximum number of scientists listed in Stanford dataset metrics were not ranked in the world university rankings table. The Times Higher Education (THE) calculate the ranking of universities under 5 categories and 17 sub-categories and each main and/or sub categories have different calculation weight which are 29.5% Teaching (15% teaching reputation, 4.5% student staff ratio, 2% Doctorate bachelor ratio, 5.5 Doctorate staff ratio, and 2.5% Institutional income); 29% Research environment (5.5% volume, 5.5% income and 18% reputation); 30% Research quality (15% citation impact, 5% research strength, 5% research excellence and 5% research influence); 7.5% International outlook (2.5% staff, 2.5% students and 2.5% research); and 4% Industry (2% income and 2% patents) (Web2, 2024). It is obvious that the top 4 universities as shown in Figure 4 were strength in research environment and research quality categories. Therefore, the top 4 universities need to increase their scores in other categories in order to rise in the Times Higher Education World university rankings.

Figure 4:
The number of ranked scientists involved in the top 25 Universities.

Nowadays, it’s critical to assess and index scientific literature. The literature has a wide range of markers for grouping and classifying scientific papers. A more complete picture of the effect may be obtained by combining many indications, but no one approach can choose the greatest scientists. Among the multiple indicators, the Stanford database metric list stands out among other indicators by considering the citations to the publications of scientists from different aspects (specifically, single, first, or last position authorships, since these positions reflect crucial contributions to the work). This study examined the rank of Indian scientists in the Stanford database metric list, their composite scores, citation counts, and their affiliated universities were also considered bibliometrically.

• India has 2939 scientists, placing it 14^th in the global Stanford dataset metrics according to career long metrics.
• From 2017 to 2023, the number of listed scientists increased 7 times, from 428 to 2939 according to career long metrics.
• In 2023, the c scores of Indian scientists for both career and single year perspective were very close to overall average values which were 2.7152 and 3.4584, respectively.
• Mechanical engineering and transportation, applied physics, artificial intelligence and image processing, energy, and materials are the most popular disciplines among over 100 Indian scientists in 2022 and 2023.
• The 6 of top 100 Indian scientists are women.
• The top 100 Indian scientists are 20% of chemists, 18% of physicists, 21% of clinical medical, and 14.5% of artificial intelligence.
• The top universities with the most scientists in the Stanford database list are also included in the Times Higher Education world university rankings table.