MathSciNet has been used by Jerrold W. Grossman to analyze the network of collaborations among mathematics in <A HREF="https://www.siam.org/pdf/news/485.pdf">Patterns of Collaboration in Mathematical Research:</A> *Apparently, the appropriate popular buzz phrase for mathematicians should be “eight degrees of separation”*.    
See also <A HREF="http://math.buffalo.edu/mad/stats/2005.research.patterns.pdf">Patterns of Research in Mathematics </A> by the same author, which has this graph of the <A HREF="https://en.wikipedia.org/wiki/Erdős_number">Erdős number</A> distribution among authors in that database:

<IMG SRC="https://ilorentz.org/beenakker/MO/Erdos.png" WIDTH="400"/>