Source-linked AI summary
An index to quantify an individual's scientific research output that takes into account the effect of multiple coauthorship
J. E. Hirsch
TL;DR
The paper addresses the h-index’s failure to account for multiple coauthorship and proposes ℏ as an alternative bibliometric indicator. It defines ℏ through citation thresholds coupled to coauthor h-core membership, then uses a practical non-self-consistent version. The paper argues that ℏ can distinguish researchers with different coauthorship patterns, while acknowledging disadvantages for junior researchers and large-group collaborators.
Problem
The h-index does not account for coauthorship patterns, motivating an indicator that can distinguish researchers with different collaboration structures without unfairly discouraging collaboration.
Method
ℏ counts an individual’s papers that meet an ℏ citation threshold and belong to each coauthor’s relevant core; the practical variant uses coauthors’ h-cores instead.
Results
The paper argues that the practical non-self-consistent ℏ is almost identical to the self-consistent index and can be calculated by hand.
Takeaways & Limitations
ℏ is proposed as an indicator for comparing scientists with different coauthorship patterns, either alone or combined with h.
Takeaways & Limitations
ℏ can disadvantage junior researchers collaborating with very senior researchers and is not useful for evaluating large-group collaborators across fields.
Abstract
from arXiv · showhide
I propose the index $\hbar$ ("hbar"), defined as the number of papers of an individual that have citation count larger than or equal to the $\hbar$ of all coauthors of each paper, as a useful index to characterize the scientific output of a researcher that takes into account the effect of multiple coauthorship. The bar is higher for $\hbar$.
I. INTRODUCTION AND DEFINITION
The paper introduces ℏ as a coauthorship-aware bibliometric index. Its self-consistent definition requires qualifying papers to meet both citation and coauthor criteria, while a non-self-consistent version is proposed for practical calculation.
- Definition: ℏ counts papers with at least ℏ citations that also belong to every coauthor’s ℏ-core.
- Definition: The self-consistent ℏ-index uniquely characterizes a scientist and cannot exceed the conventional h-index.
- Properties: For single-author researchers, ℏ equals h, although ℏ = h does not imply that all papers are single-author.
- Properties: Unlike h, the self-consistent ℏ-index assigns each paper a unique status across its authors: ℏ-contributing or non-ℏ-contributing.
- Practical variant: The non-self-consistent ℏ replaces coauthors’ ℏ values with their h values, making calculation practical while usually producing an almost identical, occasionally smaller index.
II. MOTIVATION
The paper motivates ℏ by arguing that h ignores the number and pattern of coauthors, potentially distorting comparisons and creating incentives for honorary authorship. It seeks an indicator that recognizes collaboration without unfairly dividing credit or discouraging essential collaborative work.
- Problem: The h-index ignores the number of coauthors, which can distort comparisons between researchers with very different collaboration patterns.
- Incentives: Because current indicators impose no penalty for adding authors, they may create incentives for honorary authorship through implicit or explicit quid pro quo expectations.
- Existing approaches: Existing fractional-credit modifications may discourage collaboration and treat coauthors unfairly despite unequal contributions and discipline-specific authorship conventions.
- Design criteria: A desirable indicator should support meaningful evaluation, avoid harmful incentives, resist random citation fluctuations, and remain obtainable from existing databases.
- Proposed response: The paper presents ℏ as a candidate that accounts for multiple coauthorship and can be used alone or alongside h.
III. CALCULATION OF ℏ
The calculation begins by removing h-core papers whose coauthors have higher h values than the papers’ citation counts, then rechecks lower-ranked papers to obtain the final ℏ. The procedure can be performed using citation-ranked database records and coauthor h-indices.
- First iteration: In the example, papers 18, 17, and 16 are removed because senior coauthors have h-indices exceeding those papers’ citation counts.
- First iteration: Assuming the remaining original h-core papers qualify, removing three papers reduces A’s h = 20 to ℏ_first-iteration = 17.
- Second iteration: A second iteration can add papers outside the original h-core when their citation counts meet the revised rank threshold and their coauthors’ criteria.
- Second iteration: In the example, a single-author paper with 19 citations is added, while a paper coauthored with someone whose h = 45 is excluded.
- Final calculation: The final index satisfies ℏ_first-iteration ≤ ℏ ≤ h, with every counted paper having at least ℏ citations and qualifying for the coauthors’ h-cores.
- Database procedure: The hand calculation uses citation-ranked records, paper numbers, citation counts, and coauthor h-indices, with frequent high-h coauthors checked first to simplify the process.
IV. WHY IS ℏUSEFUL?
The ℏ-index is intended to distinguish research contributions from citation advantages conferred by prominent collaborators, while preserving collaboration among similarly senior scientists. Its usefulness is tempered by greater computation time and particular disadvantages for junior researchers.
- Trade-offs: Computing ℏ is more time consuming than computing h, although the paper describes it as straightforward and feasible in most cases within minutes.The author suggests researchers can often calculate their own ℏ-index using familiarity with collaborators’ h-indices.
- Motivation and comparison: The ℏ-index is argued to counterbalance citation advantages arising from better-known senior coauthors and large research groups.For comparable h-indices, researchers whose citations derive more from prominent collaborators may have lower ℏ-indices.
- Trade-offs: The index is particularly unkind to junior researchers and is recommended alongside h and other bibliometric and non-bibliometric criteria.The paper suggests an average of h and ℏ only if a single bibliometric parameter is required.
- Motivation and comparison: Collaborations between scientists with similar h-indices are not expected to substantially reduce either collaborator’s ℏ-index.Only papers in the narrow citation interval between their h-indices can be excluded from one collaborator’s ℏ-core.
- Trade-offs: The ℏ-index can discourage honorary authorship and may decrease when a coauthor’s h-index rises sufficiently to disqualify a coauthored paper.This time-dependent behavior differs from the ordinary h-index.
- Motivation and comparison: The ℏ-index is intended to reflect leading contributions and papers important enough to enter the h-core of more senior coauthors.The paper presents this as potentially more accurate than the h-index for individual contribution assessment.
V. EXAMPLES
Examples show that ℏ can reorder researchers relative to h, often reducing scores for collaborations with more senior coauthors while preserving credit for independent work.
- Illustrative examples: A physicist with h = 17 had ℏ = 12, with contributing papers combining highly cited collaborations and senior- or sole-author work.The 12 contributing papers included papers with senior coauthors and papers where the researcher was senior or sole author.
- Illustrative examples: Scalapino had h = 81 and ℏ = h, while collaborators’ h-indices ranged from 59 to 7 and their ℏ-indices from 58 to 1.For collaborators, h−ℏ ranged from 10 to 1, reflecting collaboration with Scalapino and other senior researchers.
- Ranking reversals: Researchers with larger h can have smaller ℏ: SRW had h = 47 and ℏ = 37, whereas RLS had h = 43 and ℏ = 38.The examples show that h- and ℏ-based ranking orders can be reversed.
- Ranking reversals: Among researchers with lower h, MJM had h = 21 and ℏ = 19, exceeding NEB’s ℏ = 17 despite NEB’s h = 23.Similar reversals occurred for EJ, whose h = 18 was below several peers while ℏ = 14 exceeded their ℏ values.
- Ranking reversals: Identical h-indices can correspond to different ℏ-indices, including AM and RLS with h = 43 but ℏ values of 35 and 38.Other equal-h comparisons likewise produced distinct ℏ values: MJ, RLS, and WH had h = 34 but ℏ values of 33, 30, and 29.
- High-energy experimental physics: For a senior high-energy experimentalist with h = 44, the first iteration yielded ℏ = 17 or lower because highly cited papers were excluded due to coauthors’ higher h-indices.Four papers outside the h-core entered the ℏ-core; these were fairly recent senior- or single-author papers, indicating increasing independence.
VI. CLOSING ARGUMENTS
The paper argues that ℏ can reward independent research while retaining credit for collaboration, but its interpretation should account for career stage, field, and individual circumstances. It also identifies computational, temporal, and conceptual limitations that constrain how ℏ should be used.
- VI. CLOSING ARGUMENTS: ℏ gives full h-equivalent credit to a paper’s most senior coauthor while potentially excluding junior coauthors who receive h-index credit.Here, seniority is defined by the coauthor with the highest h-index.
- VI. CLOSING ARGUMENTS: The author argues that ℏ rewards vigorous independent research and can discourage purely political coauthorship without penalizing researchers for supervising younger collaborators.The proposed incentives are presented as beneficial to scientific progress.
- VI. CLOSING ARGUMENTS: For very young scientists, ℏ is harsh and should be combined with h, other indicators, and non-bibliometric criteria.The paper notes that collaboration with senior scientists may benefit young researchers through resources, learning, and recommendations even when ℏ provides limited short-term credit.
- VI. CLOSING ARGUMENTS: ℏ is unsuitable for interpreting researchers who routinely work in very large collaborations, except perhaps through comparisons within the same collaboration-heavy field.The paper also warns that ℏ can misrepresent individual circumstances, including cases where a junior theorist’s contribution is delayed by coauthorship with a senior experimentalist.
- VI. CLOSING ARGUMENTS: ℏ can decrease over time when former collaborators later outperform a scientist, unlike h, which does not have this behavior.The paper describes this as a potential hbar-gap dynamic during a researcher’s career.
- VI. CLOSING ARGUMENTS: The self-consistent ℏ is extremely difficult to compute, whereas the non-self-consistent version is feasible with moderate effort and is usually identical or close.The paper therefore focuses on the non-self-consistent index, which can be calculated by hand in a few minutes using database information.