In the world of mathematics, you can see networking effects in terms of your Erdős number which quantifies the series of connections through the scientific community to the published work of Paul Erdős. As well as being a prolific author of mathematical papers, Paul Erdős was also quite an enigmatic character. His biography, The Man Who Loved Only Numbers, is worth a read.
To be assigned an Erdős number, one must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is $k + 1$ where $k$ is the lowest Erdős number of any co-author.
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 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 (9267 people as of 2010), 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 Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a researcher can obtain is 2. 1)
Below is the distribution of Erdős Numbers2)
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
Checking through AMS:
http://www.ams.org/mathscinet/collaborationDistance.html
O'Brien-Huyet/McInerney-Pokrovskii-Boltyanskii-Soifer-Erdős
“Rigorous analysis of complicated behaviour in a truncated LangKobayashi model”
O. Rasskazov, G. Huyet, J. Mcinerney, A. Pokrovskii
Stephen Barnett is same or??
Huyet-Barnett-Johnson-Schönheim-Erdős
Superposition states at finite temperature
G. Huyet, S Franke-Arnold, S.M. Barnett
Arlazarov, V. L.; Uskov, A. V. Faradžev, I. A. An algorithm for finding all simple cycles in a directed graph. (Russian) Studies in discrete mathematics (Russian), pp. 178–183. Izdat.“Nauka'', Moscow, 1973.
MR Erdos Number = 4
MR2070618 34C23 (34C25 34K13 34K18) Krasnoselʹskii, A. M.; McInerney, J.; Pokrovskii, A. V. Synchronized double-frequency oscillations in a class of weakly resonant systems. Nonlinear Anal. 57 (2004), no. 7-8, 929–949.
MR Erdos Number = 4
tool From Microsoft would suggest Erdös number of 4 McInerney-H.S.Gamble-H.L.Montogmery-Erdős
doesn't look reliable though, results don't make sense.. (McInerney search does not show this link!)
~~DISCUSSION~~