Publication and Citation-based Impact

I have been collecting data on citations of my own work for a number of years and once wrote a guide to the concepts for biologists (rather than for those better versed in bibliometrics and scientometrics) (put on PeerJ Preprint Server, 2014-08-26). I have expanded the collection of metrics beyond those described in the paper and have now created a separate webpage for every metric, including a basic explanation, a worked example (in many cases), and a year-by-year history of that metric based on my own publication record.

The code for calculating all of these metrics can be found on Github.

Citation data used for calculating all examples extracted from Google Scholar on 2025-06-05.

Below the Index is a table summarizing major properties of the various indices.

Common Symbols and Definitions

• P — The total number of publications of an author. Unless otherwise specified, publications are in rank order from 1…P, with 1 having the most citations and P the fewest.
• C_i — The number of citations for the i^th publication.
• C^x — The sum of citations for the top x publications, \(C^x=\sum\limits_{i=1}^{x}{C_i}\).
• A_i — The number of authors of the i^th publication.
• a_i — The ordered position of the focal author among the full author list of the i^th publication, it's value can range from 1 to A_i.
• Y_i — The year of the i^th publication.
• Y₀ — The year of the author's first publication, \(Y_0=\min\left(Y_i\right)\).
• academic age — The number of years since an author's first publication. If Y is the current year (or year of interest), the academic age of the author is \(Y-Y_0+1\).

Index

• a-index
• academic trace
• adapted pure h-index (fractional credit)
• adapted pure h-index (geometric credit)
• adapted pure h-index (proportional credit)
• age-normalized h-index
• annual h-index
• apparent h-index
• ar-index
• a_t
• average scientific activity
• b-index (10% rate)
• b-index (mean self-citation rate)
• C/P index
• Carbon h-factor
• career years h-index by average citations per year
• career years h-index by citations
• career years h-index by diffusion speed
• career years h-index by publications
• CC
• CDR-index
• CDS-index
• C^H
• characteristic time scale of scientific activity
• CI
• circular citation area radius
• citation acceleration
• citation count
• citation distribution rate index
• citation distribution score index
• citation entropy
• citations per publication
• citations per year
• cited paper percent
• C_max
• collaborative coefficient
• collaborative index
• contemporary h-index
• corrected quality ratio
• corrected quality ratio (60:40)
• C^P
• CPP
• CQ index
• C_T
• C^TS
• D
• DC
• DCI index (mild decay)
• DCI index (sharp decay)
• dDCI index (mild decay)
• dDCI index (sharp decay)
• degree of collaboration
• dh
• discounted cumulated impact (mild decay)
• discounted cumulated impact (sharp decay)
• discounted h-index
• dynamic discounted cumulated impact (mild decay)
• dynamic discounted cumulated impact (sharp decay)
• dynamic h-type-index
• e-index
• EM′-index
• EM-index
• equally weighted h-index
• f-index (Franceschini & Maisano)
• f-index (Tol)
• first-author h-index
• fractional citation g-index
• fractional citation h-index
• fractional g-index
• fractional p-index
• fractional paper h
• g-index
• generalized impact factor
• g_F
• g_f
• H
• h′-index
• h(2)-index
• h-index
• h-norm index
• h-rate
• h²-center index
• h²-tail index
• h²-upper index
• h_A
• harmonic p-index
• h^C
• h_c
• h_e
• h_f
• h_F-index
• h_fa
• hg-index
• h_i-index
• hIa
• Hirsch core citations
• Hirsch proportionality constant
• history h-index
• H_j-indices
• h_m-index
• hⁿ
• h_p
• hpd-index
• h_r
• h_rat
• h_T
• h^t
• h^TS
• h_w
• h^Δ
• i10 index
• i100 index
• i1000 index
• I_f
• impact vitality
• indifference
• interpolated h-index
• iterative weighted EM′-index
• iterative weighted EM-index
• iteratively weighted h-index
• iw(h)-index
• iw_EM
• iw_EM′
• j-index (Levene)
• j-index (Mikhailov)
• j-index (Todeschini)
• journal paper citedness
• JPC
• k-index (Anania and Caruso)
• k-index (Ye and Rousseau)
• k-norm index
• least squares h-rate
• L^v
• m-index
• m-quotient
• m-ratio index
• maximum citations
• maxprod-index
• MCR
• mean citation rate
• mean citations per publication
• mean observed citation rate
• mean self-citation rate
• median citations per publication
• mock h_m-index
• MOCR
• multidimensional h-index
• normalized h-index
• normalized h_i-index
• o
• o-index
• observed citation rate
• OCR
• P
• p-index (P₁)
• p-index (Prathap)
• P₁
• P_C%
• p_f
• p_h
• ph-ratio
• position-weighted h-index
• profit adjusted h-index
• profit h-index
• profit p-index
• P^TS
• P_U
• P_U%
• publications per year
• pure h-index (fractional credit)
• pure h-index (geometric credit)
• pure h-index (proportional credit)
• Q
• q-index
• q²-index
• quality quotient
• R-index
• rational h-index
• real h-index
• rec-index
• rec_I, rec_P
• Redner index
• r_m-index
• s-index (citation entropy)
• S-index (h-mixed synthetic index)
• s-index (specific impact)
• scientific quality index
• scientist's level
• scientist's level (non-integer)
• sharpened h-index (narrow)
• specific impact s-index
• T-index (h-mixed synthetic index)
• t-index (Singh)
• t-index (Tol)
• tapered h-index
• t_h
• time-scaled citation index
• time-scaled h-index
• time-scaled number of publications
• total citations
• total publications
• total self citations
• total self-citation rate
• tr(V)
• trend h-index
• two-sided h-index
• UF
• uncited paper percent
• uncitedness factor
• v-index
• w(q) (Wu)
• w-index (Anania and Caruso)
• w-index (Woeginger)
• w-index (Wohlin)
• w-index (Wu)
• w-norm index
• weighted citation aggregate (fractional)
• weighted citation aggregate (proportional)
• weighted citation H-cut (fractional)
• weighted citation H-cut (proportional)
• weighted h-index
• Yc_EM
• Yc_EM′
• Year-based EM′-index by citations
• Year-based EM'-index by publication year citations
• Year-based EM′-index by publications
• Year-based EM-index by citations
• Year-based EM-index by publication year citations
• Year-based EM-index by publications
• yearly h-index
• Yp_EM
• Yp_EM′
• Ypc_EM
• Ypc_EM′
• α-index
• μ-index
• ξ_e
• ξ_p
• π-core citation rate
• π-index
• τ
• χ-index
• ψ_e
• ψ_p

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Properties Table

This table attempts to give a basic summary of some of the properties that distinguish the different metrics and measures.