H-index¶

A bibliometric index equal to the largest integer h for which an author or other publication set has at least h works cited at least h times each.

Version: v2 · 2026-09-19 · History
Domain-specific #: 4799
Domain group: Professional & Organizational Practice
Origin domain: Library & Information Science
Subdomain: Bibliometrics and Research Evaluation → Library & Information Science

Core Idea¶

The h-index combines output and citation depth in one threshold statistic but varies with field, career length, database, authorship practice, document type, and citation culture and discards information beyond the threshold. Citation counts are collected for a declared work set and source, sorted descending, and compared with their ranks; the greatest rank not exceeding its citation count is reported. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

How would you explain it like I'm…

The Paper-Pointing Score

Imagine you drew lots of pictures and friends gave each one some stickers. Your number is the biggest number where that many pictures each got at least that many stickers. If 3 pictures got at least 3 stickers each, but you don't have 4 pictures with at least 4, your number is 3. Scientists use this for how often their writings get mentioned.

The Citation Cutoff Score

When scientists write papers, other papers mention them; each mention is called a citation. To find someone's H-index, list their papers from most cited to least cited and number them 1, 2, 3, and so on. Find the last spot where the paper's number is still no bigger than its citation count. That number is the H-index. It mixes how many papers you wrote with how much they got cited, but it ignores extra citations above that cutoff, and it changes depending on which database you count from and which field you work in.

h Papers, h Citations

The H-index is a single number summarizing a researcher's (or group's) publications and citations: it's the largest h such that h of their works have each been cited at least h times. You compute it by sorting citation counts from highest to lowest and finding the last rank that doesn't exceed its citation count. Unlike a plain citation total, it rewards having many well-cited papers rather than one hit. But it throws away information—a paper with 1,000 citations counts the same as one just above the threshold. It also changes depending on the field, career length, which database is used and when, how co-authorship and document types are handled, and the citation habits of the field.

The H-index is a threshold statistic in bibliometrics combining output and citation impact. For a declared entity and publication set, citation counts are drawn from a specified database at a specified date, sorted in descending order, and compared with their ranks; h is the greatest rank r such that the r-th work has at least r citations. It thus requires h works with ≥h citations each. Because it is a threshold, it discards citations above h for top works and ignores works below the cutoff. Its value depends on field, career length, database coverage, document-type and authorship rules, and citation culture, so comparisons across these contexts are unreliable. A proper report states the entity, work set, source and date, counting rules, and the field and career context.

Scope of Application¶

H-index belongs to bibliometrics and research evaluation and is useful where the analyst can specify the typed bibliometrics and research evaluation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context are explicit. The scope is broad within that domain but bounded by the need for the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context are explicit. Descriptive bibliometric identity only; it is not a sufficient measure of researcher quality, hiring merit, funding priority, or institutional performance.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name H-index can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to H-index. H-index compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed bibliometrics and research evaluation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
Lock the constitutive rule. Express the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of bibliometrics and research evaluation because they reuse the typed bibliometrics and research evaluation carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Citation counts are collected for a declared work set and source, sorted descending, and compared with their ranks; the greatest rank not exceeding its citation count is reported., and type the carrier, state every parameter and convention in the definition, test that the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction H-index Domain-specific

Parents (1) — outgoing typed relations

H-index is a kind of Threshold Prime

It remains its own entry because its identity is fixed by the evaluated entity, publication set, citation database and date, document and authorship rules, sorted counts, threshold calculation, and field and career context.

Hierarchy path (1) — routes to 1 parentless root

H-index → is a kind of Threshold

Neighborhood in Abstraction Space¶

H-index sits in a crowded region of the domain-specific corpus (39^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Research Design & Measurement Bias (23 abstractions)

Nearest neighbors

Acknowledgment index — 0.88
Round-robin test — 0.87
Free scientific research — 0.87
Testing hypotheses suggested by the data — 0.87
Designated Member Review — 0.87

Computed from structural-signature embeddings · 2026-10-25