Metric Studies in LIS: Bibliometrics, Scientometrics, Webometrics and Altmetrics; the Laws of Lotka, Bradford and Zipf; Journal, Institutional and Author Impact Measures with the h-Index, g-Index and i10-Index Worked; and Trends in LIS Research

The metric study of literature is one of the few research fields that library and information science can call its own, and nothing on this platform covers it elsewhere. This chapter takes Unit IX's items 8 to 10: bibliometrics, scientometrics, webometrics and altmetrics, with the classic laws of Lotka, Bradford and Zipf worked with numbers; citation analysis; impact measures for journals, institutions and authors, including a two-year journal impact factor calculated step by step and the h-index, g-index and i10-index computed from one citation list; and the trends now shaping research in the discipline. Every answer below has been worked and checked.

1. Bibliometrics, scientometrics, webometrics and altmetrics

FieldOriginWhat it measures
BibliometricsTerm coined by Alan Pritchard (1969) for the application of mathematics and statistical methods to books and other media of communication; earlier "statistical bibliography" (E. Wyndham Hulme, 1923) and Ranganathan's "librametry" (1948)Publications, authors, journals, citations and their distributions
ScientometricsFrom the Russian naukometriya of V. V. Nalimov and Z. M. Mulchenko (1969); the journal Scientometrics was founded in 1978Science as a system: research output, collaboration, growth, impact and science policy indicators
InformetricsTerm used by Otto Nacke (1979); the umbrella for quantitative studies of information in any formAll of the above, plus information retrieval and use
WebometricsTomas Almind and Peter Ingwersen (1997); Ingwersen proposed the Web Impact Factor (1998)Web pages, links, sites and search engine data; also used in webometric rankings of universities
AltmetricsProposed by Jason Priem; "Altmetrics: a manifesto" by Priem, Taraborelli, Groth and Neylon (2010); providers include Altmetric.com (with its Attention Score) and PlumXOnline attention to research: mentions in news, policy documents, blogs, social media, Wikipedia, and saves in reference managers such as Mendeley

Citation analysis studies the links between citing and cited documents. Bibliographic coupling (M. M. Kessler, 1963) links two papers that cite the same earlier paper; their coupling strength is the number of references they share, and it is fixed once they are published. Co-citation (Henry Small and, independently, Irina Marshakova, 1973) links two papers that are cited together by later papers; its strength grows as the literature grows, so it maps how a field sees its own structure. Other key ideas are Derek de Solla Price's observation in Little Science, Big Science (1963) that scientific literature grows exponentially, doubling roughly every 10 to 15 years; Price's law, that about half of all papers in a field come from the square root of the number of authors; obsolescence, measured by the half-life of literature (Burton and Kebler, 1960); and the Matthew effect (Robert Merton, 1968), by which well-known scientists receive disproportionate credit.

⚠️ Coupling looks back; co-citation looks forward
Bibliographic coupling is decided by the papers' own reference lists, so it is fixed at publication. Co-citation is decided by what later authors cite, so it changes over time. If papers A and B both cite C, A and B are bibliographically coupled; if a paper D cites both A and B, A and B are co-cited.

2. The laws of Lotka, Bradford and Zipf, worked

LawStatementWorked example
Lotka's law (Alfred Lotka, 1926): author productivityThe number of authors making n contributions is about 1/n² of the number making one: an inverse square law. About 60 per cent of authors in a field contribute only one paperIf 100 authors write one paper each, about 100/2² = 25 write two, 100/3² ≈ 11 write three and 100/4² ≈ 6 write four
Bradford's law of scattering (Samuel Bradford, 1934): journal productivityIf journals are ranked by the number of articles they carry on a subject and divided into a nucleus and successive zones each yielding about the same number of articles, the numbers of journals in the zones are in the ratio 1 : n : n², where n is the Bradford multiplierA nucleus of 5 journals with multiplier 3 gives zones of 5, 15 and 45 journals, 65 in all, each zone carrying about a third of the articles
Zipf's law (George Kingsley Zipf, 1949): word frequencyIn a long text, a word's frequency is roughly inversely proportional to its rank: rank × frequency ≈ a constantIf the commonest word occurs 6,000 times, the third commonest occurs about 6,000/3 = 2,000 times and the tenth about 600 times

Each law has a practical use. Lotka's law shows that a small core of prolific authors produces much of a field's literature, which matters for collection building and for evaluating research. Bradford's law is the basis of core-journal collection policy: a library can hold the nucleus of highly productive journals and obtain the scattered remainder through inter-library loan or document delivery, and it explains why comprehensive coverage becomes steeply more expensive. Zipf's law underlies stop-word lists and term weighting in automatic indexing: the most frequent words carry little meaning, and mid-frequency words discriminate best between documents. Together the three are sometimes called the three classic bibliometric laws, and all describe highly skewed distributions in which a few sources account for most of the output.

🧠 Which law is about what?
Lotka counts authors (productivity), Bradford counts journals (scattering), Zipf counts words (frequency). The years run 1926, 1934, 1949, in the same order as the list.

3. Journal impact measures

Eugene Garfield proposed citation indexing in 1955 and, with Irving Sher, the journal impact factor, published in the Journal Citation Reports from 1975, now produced by Clarivate. The two-year journal impact factor for year Y is the number of citations received in year Y by items the journal published in the two previous years, divided by the number of citable items (articles and reviews) it published in those two years. Worked example: in 2023 a journal published 120 citable items and in 2024 it published 130, 250 in all. During 2025, items from 2023 were cited 360 times and items from 2024 were cited 240 times, 600 citations in all. Its 2025 impact factor is 600 ÷ 250 = 2.4. Related Clarivate measures are the five-year impact factor, the immediacy index (citations in year Y to items published in year Y, divided by the number of those items) and the cited half-life. From its 2023 release the Journal Citation Reports gives impact factors to all journals in the Web of Science Core Collection, reported to one decimal place.

MeasureSource and basis
Journal impact factor (JIF)Clarivate, Web of Science; citations in one year to the previous two years' items
CiteScoreElsevier, Scopus, from 2016; since 2020 citations over four years to documents published in those same four years, divided by those documents
SJR (SCImago Journal Rank)SCImago, from Scopus data; weights citations by the prestige of the citing journal
SNIP (Source Normalized Impact per Paper)Henk Moed, CWTS Leiden; corrects for differences in citation practice between fields
EigenfactorCarl Bergstrom and colleagues; a network-based measure over five years that excludes journal self-citations
🎯 Why a journal's impact factor says little about one paper
Citations to a journal are highly skewed: a few papers collect most of them, so the average hides wide variation, and citation rates differ greatly between fields. The San Francisco Declaration on Research Assessment (DORA, 2012) and the Leiden Manifesto (2015) warn against using journal-based measures to judge individual researchers.

4. Author and institutional measures: h-index, g-index and i10-index

J. E. Hirsch proposed the h-index in 2005: a researcher has index h if h of his or her papers have at least h citations each and the remaining papers have no more than h each. Leo Egghe's g-index (2006) gives more weight to highly cited papers: it is the largest number g such that the top g papers together have at least g² citations. Google Scholar introduced the i10-index in 2011: the number of papers with at least 10 citations. Hirsch's m-quotient divides h by the number of years since the researcher's first paper, to compare careers of different lengths.

h-index = 6, because the 6th paper has 6 citations (at least 6) but the 7th has only 5; g-index = 9, because the top 9 papers have 88 citations, at least 81, but the top 10 still have 88, fewer than 100; i10-index = 4, the papers with 25, 18, 12 and 10 citations; total citations 88
Rank of paperCitationsCumulative citationsRank squared
125251
218434
312559
4106516
587325
667936
758449
838764
918881
10088100

Institutional measures aggregate the output of an institution: numbers of publications, citations per paper, field-normalised citation impact, the share of papers among the most highly cited, international collaboration, and an institutional h-index. They feed rankings such as the Leiden Ranking (CWTS), the SCImago Institutions Rankings, the Times Higher Education and QS rankings, and India's National Institutional Ranking Framework (NIRF), launched by the Ministry of Education in 2015 with its first rankings in 2016, whose research and professional practice parameter draws on publications and citations. The h-index is easy to compute but ignores citations beyond h, favours long careers and varies by field and database (Web of Science, Scopus and Google Scholar give different values for the same person).

Key takeaways

  • Bibliometrics (Pritchard, 1969), scientometrics (Nalimov and Mulchenko, 1969), informetrics (Nacke, 1979), webometrics (Almind and Ingwersen, 1997) and altmetrics (Priem and others, 2010); bibliographic coupling (Kessler, 1963) is fixed, co-citation (Small; Marshakova, 1973) grows.
  • Lotka (1926): authors with n papers ≈ 1/n² of those with one (100 single-paper authors imply about 25 with two); Bradford (1934): zones of journals 1 : n : n² (5, 15, 45 for n = 3); Zipf (1949): rank × frequency ≈ constant.
  • The two-year JIF = citations in Y to items from Y−1 and Y−2 ÷ citable items from Y−1 and Y−2 (600 ÷ 250 = 2.4); others are CiteScore (four-year window since 2020), SJR, SNIP and Eigenfactor; DORA and the Leiden Manifesto caution against misuse.
  • h-index (Hirsch, 2005), g-index (Egghe, 2006) and i10-index (Google Scholar, 2011): for citations 25, 18, 12, 10, 8, 6, 5, 3, 1, 0 they are 6, 9 and 4; institutional measures feed rankings including NIRF (2015, first rankings 2016).
  • LIS research trends: research data, AI, open science and responsible metrics, science mapping (VOSviewer, CiteSpace, bibliometrix), information behaviour and UX, digital humanities and linked data, and mixed methods.

Practice questions (10)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. A researcher's ten papers have 25, 18, 12, 10, 8, 6, 5, 3, 1 and 0 citations. What is the h-index? Type the number.

    Numerical answer — type the value.

    Show answer

    Answer: 6

    Ranked in descending order, the 6th paper has 6 citations, which is at least 6, but the 7th has 5, which is less than 7. So six papers have at least six citations each and h = 6.

  2. For the same citation list (25, 18, 12, 10, 8, 6, 5, 3, 1, 0), what is the g-index? Type the number.

    Numerical answer — type the value.

    Show answer

    Answer: 9

    Cumulative citations of the top g papers must be at least g². Top 9: 25 + 18 + 12 + 10 + 8 + 6 + 5 + 3 + 1 = 88, which is at least 9² = 81. Top 10: still 88, less than 10² = 100. So g = 9.

  3. A journal published 120 citable items in 2023 and 130 in 2024. In 2025 those items received 360 and 240 citations respectively. What is its 2025 journal impact factor? Type the number.

    Numerical answer — type the value.

    Show answer

    Answer: 2.4

    JIF 2025 = citations in 2025 to 2023 and 2024 items ÷ citable items of 2023 and 2024 = (360 + 240) ÷ (120 + 130) = 600 ÷ 250 = 2.4.

  4. By Lotka's inverse square law, if 900 authors in a field each wrote exactly one paper, about how many authors wrote exactly three papers? Type the number.

    Numerical answer — type the value.

    Show answer

    Answer: 100

    Authors with n papers ≈ authors with one paper ÷ n². For n = 3: 900 ÷ 3² = 900 ÷ 9 = 100. For comparison, about 900 ÷ 4 = 225 would have written two.

  5. Under Bradford's law, the nucleus of core journals on a subject contains 6 journals and the Bradford multiplier is 3. How many journals are in the third zone? Type the number.

    Numerical answer — type the value.

    Show answer

    Answer: 54

    Zones are in the ratio 1 : n : n², so with a nucleus of 6 and n = 3 they hold 6, 6 × 3 = 18 and 6 × 3² = 54 journals, 78 in all, each zone yielding about the same number of articles.

  6. Who coined the term "bibliometrics" in 1969?

    1. S. R. Ranganathan
    2. Eugene Garfield
    3. Alan Pritchard
    4. Peter Ingwersen
    Show answer

    Answer: C — Alan Pritchard

    Alan Pritchard proposed "bibliometrics" in 1969 to replace "statistical bibliography". Ranganathan had suggested "librametry" in 1948, Garfield founded citation indexing, and Ingwersen co-founded webometrics.

  7. Zipf's law states that in a large body of text:

    1. Literature doubles every year
    2. Journals fall into zones in the ratio 1 : n : n²
    3. The number of authors with n papers is 1/n² of those with one
    4. A word's rank multiplied by its frequency is roughly constant
    Show answer

    Answer: D — A word's rank multiplied by its frequency is roughly constant

    Zipf's law concerns word frequency: rank × frequency ≈ constant. The inverse square law of authors is Lotka's, the 1 : n : n² zones are Bradford's, and Price estimated that scientific literature doubles every 10 to 15 years, not every year.

  8. Assertion (A): The bibliographic coupling strength of two published papers does not change over time. Reason (R): Bibliographic coupling is measured by the number of references the two papers share, which is fixed when they are published. Choose the correct option.

    1. Both A and R are true, and R is the correct explanation of A
    2. Both A and R are true, but R is not the correct explanation of A
    3. A is true, but R is false
    4. A is false, but R is true
    Show answer

    Answer: A — Both A and R are true, and R is the correct explanation of A

    Both are true and R explains A. Coupling depends only on the papers' own reference lists, which do not change after publication; co-citation, by contrast, depends on later citing papers and grows over time.

  9. Which of the following are journal-level impact measures? Select all that apply.

    1. i10-index
    2. g-index
    3. CiteScore
    4. SNIP
    Show answer

    Answer: C — CiteScore; D — SNIP

    CiteScore (Scopus) and SNIP (CWTS Leiden) rate journals. The i10-index and g-index are author-level measures of a researcher's papers.

  10. Which of the following are sources of altmetric data? Select all that apply.

    1. Saves in Mendeley libraries
    2. Mentions in news stories and policy documents
    3. The two-year journal impact factor
    4. Social media posts about a paper
    Show answer

    Answer: A — Saves in Mendeley libraries; B — Mentions in news stories and policy documents; D — Social media posts about a paper

    Altmetrics track online attention: news and policy mentions, reference-manager saves and social media. The journal impact factor is a traditional citation-based measure of journals, the very thing altmetrics were proposed to complement.