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 2025-08-19.

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.
  • Ci — The number of citations for the ith publication.
  • Cx — The sum of citations for the top x publications, \(C^x=\sum\limits_{i=1}^{x}{C_i}\).
  • Ai — The number of authors of the ith publication.
  • ai — The ordered position of the focal author among the full author list of the ith publication, it's value can range from 1 to Ai.
  • Yi — The year of the ith 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

Properties Table

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