The h-index is used to gauge a researcher's productivity. If Dr. Amar has…
2025
The h-index is used to gauge a researcher's productivity. If Dr. Amar has published five papers with the following citation counts: 21, 12, 4, 2 and 1, then what is the h-index of Dr. Amar?
Answer: B. 3 — ConceptThe h-index is a single number that combines how much a researcher publishes with how often that work is cited. A researcher has an h-index of h when h…
- A.
4
- B.
3
- C.
5
- D.
10
Show answer & explanation
Correct answer: B
Concept
The h-index is a single number that combines how much a researcher publishes with how often that work is cited. A researcher has an h-index of h when h of their papers have each been cited at least h times, while every remaining paper has been cited no more than h times. The value is therefore capped twice over: it can never exceed the total number of papers published, and it can never exceed the citation count of the paper sitting at that rank. Extra citations on an already-qualifying paper add nothing — the measure rewards a consistent body of cited work rather than one heavily cited item.
Application
Arrange the five citation counts in descending order — 21, 12, 4, 2, 1 — and then test each candidate value of h in turn against the definition.
h = 1 requires 1 paper cited at least 1 time. The highest-cited paper has 21 citations, so the condition holds.
h = 2 requires 2 papers each cited at least 2 times. The top two papers have 21 and 12 citations, so the condition holds.
h = 3 requires 3 papers each cited at least 3 times. The top three papers have 21, 12 and 4 citations, every one of which is at least 3, so the condition holds.
h = 4 requires 4 papers each cited at least 4 times. The top four papers are 21, 12, 4 and 2 — the fourth of these has only 2 citations, which is below 4, so the condition fails.
h = 5 requires all 5 papers cited at least 5 times. The list contains papers cited 4, 2 and 1 times, so the condition fails.
The largest value of h that satisfies the definition is 3. Hence the h-index of Dr. Amar is 3.
Cross-check
The same result follows from a ranked table: walk down the citation counts sorted in descending order and find the last rank at which the citation count is still at least as large as the rank itself.
Rank | Citations | Citations at least equal to rank? |
|---|---|---|
1 | 21 | Yes |
2 | 12 | Yes |
3 | 4 | Yes |
4 | 2 | No |
5 | 1 | No |
The last row that still satisfies the comparison is rank 3, confirming the value obtained by direct testing. Notice also that the papers cited 21 and 12 times count exactly as much as the paper cited 4 times towards this measure: once a paper clears the threshold, further citations do not raise the h-index, which is why a single blockbuster paper cannot lift the figure on its own.