Impact Factors! Hirsch, Erdős and Pauling

Having spent 2 hours tidying CML Schema over a flaky CVS connection to sourceforge, I need some relaxation. So, after my disillusionment with the accuracy of citation metrics, I was spooking around Wikipedia and came across the h-index ( suggested in 2005 by Jorge E. Hirsch of the University of California, San Diego). This is rather similar to Zipf’s law – so essential in understanding informatics. The h-index is defined as:

A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np – h) papers have at most h citations each.

WP continues:

In other words, a scholar with an index of h has published h papers with at least h citations each. Thus, the H-index is the result of the balance between the number of publications and the average citations per publication. The index is designed to improve upon simpler measures such as the total number of citations or publications, to distinguish truly influential scientists from those who simply publish many papers. The index is also not affected by single papers that have many citations. The index works properly only for comparing scientists working in the same field; citation conventions differ widely among different fields.

So if a scientist has (say) 10 papers with citations:
200, 15, 12, 8, 5, 4, 2, 1, 0, 0
they have an h-index of 5 (5 papers have >=5 citations). The 200 citations are no more powerful than 20 would be for the first paper. If we have to have citation analysis this might be a good approach (since we have little idea how the actual numbers are obtained or who is using what) and the parametric approach allows for this. (I have yet to find how a “citation” is defined). (BTW if it matters I score ca 14 on Google Scholar – Feynmann is quoted at 23, Hawking at 68 – don’t take it too seriously – Galois scores 2).
Anyway, now for some light vanity. In the links to h-index was the Erdős number. This is named after the legendary Hungarian mathematician who was prolific both in the number of his papers and his collaborators. The number is defined as:

In order to be assigned an Erdős number, an author must co-write a mathematical paper with an author with a finite Erdős number. Paul Erdős has an Erdős number of zero. If the lowest Erdős number of a coauthor is X, then the author’s Erdős number is X + 1.


Erdős wrote around 1500 mathematical articles in his lifetime, mostly co-written. He had 504 direct collaborators; these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (6,984 people), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an undefined (or infinite) Erdős number.

So might I have a finite Erdős number? We’ve all heard how small the world is – (Six degrees of separation and Small-world network).
But very unlikely. I have to have written a mathematical paper with someone with a finite Erdős number. So I was browsing through the Erdős 4 numbers and suddenly saw Linus Pauling (Now of course I have to take WP on trust that this is a genuine entry – I can imagine the debate over Erdős numbers can be quite detailed). So could I make a chain which links to Linus Pauling (I’ve had the honour to meet him)?
Well, I searched Google scholar for L Pauling (there is also Peter Pauling, his son). And I reckoned there might be a crystallographic chain that connected me. The best I can do is:

  • Pauling + Vernon Schomaker
  • Schomaker + Jack Dunitz
  • Jack Dunitz + PeterMR

That would give me an Erdős number of 7. But, unfortunately, although my paper with Jack was mathematical (cokernels of crystallographic point groups) the Schomaker-Dunitz papers were on electron diffraction (cyclobutane, etc.) and the Pauling-Schomaker papers included the splendid title:
The Use of Punched Cards in Molecular Structure Determinations I. Crystal Structure Calculations
So, reluctantly, unless I can find another chain of mathematical papers I don’t have a finite Erdős number.
But I do have a finite Pauling number – currently 3. (I doubt I can get it lower). And since Pauling is generally acknowledged as the greatest chemist of the twentieth century, why don’t we start a Pauling number?
(Oh – FWIW  Erdős  has an h-number of 54 on Google and Pauling 39. But don’t take these too seriously).

This entry was posted in general. Bookmark the permalink.

3 Responses to Impact Factors! Hirsch, Erdős and Pauling

  1. Bill says:

    According to Google Scholar, this is me: [18,16,16,12,10,9,8,5,5,2,1,1,0,0], which yields an h-index of 7 if I understand the definition. According to the Wikipedia article, a “modestly productive” biomed researcher should have an h-index greater than their “years of service”. Even if those years start when I first published (1995), I’m not doing very well. But I didn’t need a fancy index to tell me that.

  2. you might find this H-index calculator useful to search the impact of individual scientists
    H-Index calculator that tap into the data of Google Scholar

  3. Pingback: Unilever Centre for Molecular Informatics, Cambridge - The Pauling Blog « petermr’s blog

Leave a Reply

Your email address will not be published. Required fields are marked *