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

• Alexei V. Pokrovskii coauthored with Vladimir Grigorʹevich Boltyanskii MR0862446 (88a:93001)
• Vladimir Grigorʹevich Boltyanskii coauthored with Alexander Soifer MR1104655 (92f:52031)
• Alexander Soifer coauthored with Paul Erdős1 MR1214695

Stephen Barnett is same or?? Huyet-Barnett-Johnson-Schönheim-Erdős
Superposition states at finite temperature G. Huyet, S Franke-Arnold, S.M. Barnett

• Stephen Barnett coauthored with Charles R. Johnson MR0943760 (89c:15005)
• Charles R. Johnson coauthored with Johanan Schönheim MR0705965 (84j:15007)
• Johanan Schönheim coauthored with Paul Erdős1

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

• A. V. Uskov coauthored with I. A. Faradzhev MR0412019 (54 #148)
• I. A. Faradzhev coauthored with Mikhail H. Klin MR0617203 (82g:20012)
• Mikhail H. Klin coauthored with Peter J. Cameron MR1920405 (2003f:20001)
• Peter J. Cameron coauthored with Paul Erdős1 MR1106651 (92g:11010)

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

• J. G. McInerney coauthored with Alexander M. Krasnoselʹskii MR2070618
• Alexander M. Krasnoselʹskii coauthored with Vladimir Grigorʹevich Boltyanskii MR0862446
• Vladimir Grigorʹevich Boltyanskii coauthored with Alexander Soifer MR1104655
• Alexander Soifer coauthored with Paul Erdős1 MR1214695

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~~