e-Index (Excess Citations)
Also known as: Zhang e-index, excess citation index, e index
The e-index, proposed by Chun-Ting Zhang in 2009, isolates the citations that the h-index throws away. Inside the h-core of an author's h most-cited papers, the h-index implicitly credits each paper with only h citations and discards everything above that, even though top papers may have far more. The e-index recovers exactly this surplus: it is the square root of the difference between the total citations of the h-core and the h-squared citations that the h-index already accounts for. Zhang designed it as a complement rather than a replacement for the h-index, so that the pair (h, e) together describe both the size of an author's productive core and the concentration of excess impact within it.
Key highlights
- Captures exactly the excess citations the h-index discards within the h-core, recovering information about top-paper impact.
- Designed as a complement to the h-index, so the pair (h, e) separates breadth of the core from concentration of impact.
- Placed on the same scale as h through the square root, making the two numbers easy to read together.
- Discriminates sharply among authors with identical h-indices but very different citation distributions in their best papers.
Intuition
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How it works
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When to use it
Use the e-index whenever the h-index alone is too coarse because it discards the excess citations of an author's best papers, particularly when comparing researchers who share the same or similar h-indices but differ in how heavily their top papers are cited. It is well suited to evaluations of individual scientists where the influence of standout articles should be visible, and it is most informative reported as the pair (h, e). It is not field-normalized, so it should not be used for cross-disciplinary ranking, and it is undefined or uninformative for authors with very small h-cores. Like other h-variants it depends on a clean, correctly attributed publication record.
Strengths & limitations
- Captures exactly the excess citations the h-index discards within the h-core, recovering information about top-paper impact.
- Designed as a complement to the h-index, so the pair (h, e) separates breadth of the core from concentration of impact.
- Placed on the same scale as h through the square root, making the two numbers easy to read together.
- Discriminates sharply among authors with identical h-indices but very different citation distributions in their best papers.
- Measures only citations inside the h-core, ignoring impact from papers below the h threshold.
- Not field-normalized, so it is unsuitable for fair comparison across disciplines.
- Inherits the h-index's reliance on accurate, deduplicated author publication and citation data.
- Less intuitive than a simple count, since it involves a square root of a difference and is rarely reported by default in citation databases.
Common pitfalls
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Applications
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Frequently asked
What does the e-index measure?
The e-index measures the excess citations within the h-core that the h-index ignores. The h-index credits each of the h core papers with only h citations, accounting for h-squared in total, but the core papers usually have many more. The e-index is the square root of the difference between the true total citations of the h-core and h-squared, capturing exactly this discarded surplus on a scale comparable to h.
Why is the e-index a complement to the h-index rather than a replacement?
Zhang deliberately designed e to be reported together with h rather than instead of it. The h-index conveys the breadth of an author's productive core, while the e-index conveys the concentration of excess impact within that core. Reported as the pair (h, e), the two numbers are largely non-redundant and together describe the citation distribution far better than either alone, which is why Zhang argued the e-index is needed to compare different authors' h-cores.
When is the e-index not appropriate?
The e-index only reflects citations inside the h-core, so it ignores impact from an author's many moderately cited papers below the h threshold. It is also not field-normalized, making it unfair across disciplines with different citation rates, and it can be uninformative for authors with very small h-cores. It should be read alongside the h-index and field-aware indicators rather than used as a standalone cross-field ranking tool.
Sources
- 1.Zhang, C.-T. (2009). The e-index, complementing the h-index for excess citations. PLoS ONE, 4(5), e5429.
- 2.Hirsch, J. E. (2005). An index to quantify an individual's scientific research output. Proceedings of the National Academy of Sciences, 102(46), 16569-16572.
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Cite this page
ScholarGate. (2026, June 23). e-Index (Excess Citations). ScholarGate. https://scholargate.app/bibliometrics/e-index