Adventures in coauthorship networks: my Erdős number

Photo: Paul Erdős. (c) Topsy Kretts, CC BY 3.0

Warning: very nerdy.

 Sometimes I get distracted and go down a rabbithole.  Sometimes the result is fun.

I’ve been lucky, over my career, to have a large number of coauthors (some of whom are good friends; but many of whom I’ve never even met).  Coauthorhip makes my work better, but it has other benefits too.  A somewhat abstract one is that it makes me feel that I’m part of something larger than my own research program, or even my own discipline.  I belong (as we all do) to a global and cross-disciplinary network of collaborating scientists.  And to prove it, I have an Erdős number. 

Paul Erdős (1913-1996) was a Hungarian mathematician who published somewhere around 1,500 papers (in mostly pure-math fields including set theory and number theory) and had somewhere around 500 coauthors.  He was a fascinating figure, and his biography The Man Who Loved Only Numbers is a great read.  He was famous both for brilliance and for broad collaboration.  Those two things in combination inspired mathematicians to invent the Erdős number as a metric of their collaborative closeness to Erdős.  Here’s how it works: Erdős’s own Erdős number is E = 0; those who have coauthored research papers with Erdős have E = 1; those who have coauthored with an E = 1 scientist have, as a result, E=2, and so on.

What, I wondered, was my own Erdős number?  I knew I probably had one, because an interesting property of networks is that given a surprisingly low degree of connectedness, there tend to be pathways from most nodes to most other nodes.  I also knew it probably wasn’t that large: another interesting property of networks is that internodal paths are often surprisingly short. (If someone has an Erdős number at all, it’s normally less than about 10-15.)  If you know me at all, you’ll be unsurprised that I wanted to pin this down.

Turns out, to my considerable surprise, that my Erdős number is 3.

To put that in perspective: Richard Feynman’s Erdős number is also 3; so is Andrew Wiles’s.  Erwin Schrödinger, Francis Crick, Harry Kroto, Linus Pauling, and John Nash all have E = 4.  George Smoot has E = 5, and Peter Higgs has a lovely boson and a lovely Nobel Prize, but an unimpressive E = 9.  The average for Fields Medal winners is 3.2, and the average for Nobel Prize winners (excluding Peace) is 5.3.

And yes, I know this means absolutely nothing; but again, my Erdős number is 3.

So how on Earth did I acquire E = 3?  Actually, this surprised me, because when I calculated my Erdős number I intended to cheat.  Back in 2004, I coauthored a paper with Stephen Hawking.  Yes, that Stephen Hawking; but no, not a real paper – it was a joke piece, with a huge author list, in the Annals of Improbable Research (you can read about it here).  I figured if I bent the rules and counted this as a coauthored paper, I’d get myself a nice small Erdős number.  Turns out, though, Hawking’s Erdős number is a good-but-not-awesome E = 4.  But Steven Weinberg, the 1979 Physics Nobelist, was also a coauthor and has E = 3.  That gave me E = 4, equalling Hawking, which made me pretty happy.

But then on a whim I plugged myself into the American Mathematical Society’s Erdős number calculator and discovered that I don’t have to cheat.  Based on my real papers and coauthors, I have E = 3 because:

• In 2007 I coauthored a book chapter with Michael Blum (Mooers, AØ, LJ Harmon, MGB Blum, DHJ Wong, SB Heard. Some models of phylogenetic tree shape. In Reconstructing evolution, 149–170, Oxford Univ. Press, Oxford); and
• In 2006, Michael Blum coauthored a paper with Svante Janson (Blum, MGB, O François, S Janson. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance. Ann. Appl. Probab. 16: 2195–2214.); and
• in 1996, Svante Janson coauthored a paper with Paul Erdős (Erdős, P, S Janson, T Łuczak, J Spencer. A note on triangle-free graphs. Random discrete structures. IMA Vol. Math. Appl., 76:117-119, Springer, New York).

Again, this doesn’t mean anything; but it’s pretty cool (for a spectacularly nerdy definition of “cool”).  And if you’ve ever coauthored with me*, then your Erdős number is at most 4 (and you’re welcome).

So: anybody got me beat?  Are there E = 2’s in ecology and evolution (besides, of course, Michael Blum)? Who else can join me at E = 3?**

Now if only I had an Erdős-Bacon-Sabbath number.  That would be cool.

© Stephen Heard  January 8, 2018

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*^Or with Arne Mooers or Luke Harmon or Dennis Wong – but this post is my self-indulgence, not theirs.

**^ To find your own Erdős number, you can try the American Mathematical Society calculator, but its journal coverage outside math is badly incomplete.  There are further computation tips at the Erdős Number Project home page.

 

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