Pharmacologists can be well-connected.

John J. Abel is regarded as the founding father of pharmacology, after forging the field in the late 19th century. Along with 18 colleagues, he founded American Society of Pharmacology and Experimental Therapeutics (ASPET), and is most famous for his work isolating epinephrine and crystallizing insulin. Abel published nearly a hundred papers.

Check out “Six degrees of pharmacology: Game ranks researchers by proximity to field’s founder,” an article from news @ nature.com by Jill U. Adams. You can go through the Cornell library, or if you are a nature.com subscriber go here.

As the article explains:

These papers are shared with a total of 27 co-authors, who, in the new game, are assigned an ‘Abel number’ of 1. Those 27 scientists co-published with at least 278 individuals (who get an Abel number of 2), who in turn published with at least 3,000 more (Abel number 3s).

In celebration of their 100^th anniversary in 2008, ASPET is now trying to find the Abel numbers of the rest of the pharmacology community (see ASPET website).

Despite the rivalry that resulted at the Experimental Biology meeting where this game was played, in reality these Abel numbers are more about a person’s connections than any creditable reputation. It is a family tree of pharmacologists, one that gives the field some comradeship and gives ASPET a good hundred years of traceable history.

This game is similar to the Six Degrees of Kevin Bacon game (see earlier blog post), or more similar to the game of mathematicians, who have an Erdös number that shows how close they are to the Hungarian mathematician Paul Erdös, who was famous for his huge number of collaborators (over 500) and for being one of the most prolific publishers of mathematical papers in history (around 1,500). Read about The Erdös Number Project, a project with a LOT of interesting detail.

The Erdös number study has an abundance of data and discussion available thanks to the head of the project, Jerry Grossman at Oakland University. In the Erdös numbers distribution, almost every mathematician with a number has a number of less than 8, with only about 2% higher, and none over 15. This goes to show the connectivity of the network of mathematicians.

As represented partially in the image above, the data starts with a collaboration graph (C) of about 401,000 authors, with edges that represent co-authors of papers. Without including multiple edges between two author who collaborated multiple times, the graph has 676,000 edges, with the average number of collaborators per person equaling 3.36. As in many connected graphs, there is a large group of well-connected authors. As the website explains:

In C there is one large component consisting of about 268,000 vertices. Of the remaining 133,000 authors, 84,000 of them have written no joint papers (these are isolated vertices in C). The average number of collaborators for people who have collaborated is 4.25; the average number of collaborators for people in the large component is 4.73; and the average number of collaborators for people who have collaborated but are not in the large component is 1.65.

There are then 5 people, including Erdös, with more than 200 coauthors. These well-connected people are the celebrities that make the graph bigger, and the interconnections smaller. The approximate average distance between two vertices is 7.64. As average path lengths are small, and the “clustering coefficient” of this C graph is high (0.14), the graph can be considered one of Duncan Watt’s “small-world” graphs.

      Erdös number  0  —      1 person

      Erdös number  1  —    504 people

      Erdös number  2  —   6593 people

      Erdös number  3  —  33605 people

      Erdös number  4  —  83642 people

      Erdös number  5  —  87760 people

      Erdös number  6  —  40014 people

      Erdös number  7  —  11591 people

      Erdös number  8  —   3146 people

      Erdös number  9  —    819 people

      Erdös number 10  —    244 people

      Erdös number 11  —     68 people

      Erdös number 12  —     23 people

      Erdös number 13  —      5 people

The median Erdös number is 5; the mean is 4.65, and the standard deviation is 1.21.

How amusing that one of Erdös’s specialties was actually… graph theory. I wonder if either of our own professors might have a notable Erdös number? There are two Kleinbergs on the list of 8674 people with a distance of 2 or less, but alas, no Jons.