Node connection strength in MathTree.
Each node in MathTree can be characterized by its mean distance from every other node. Below is a histogram of mean distances for every node in the tree. The final bin includes nodes that are not connected to the main tree. Note also that only individuals whose primary affiliation is this tree are included. Nodes cross-listed from other academic trees are included on their primary tree.

Mean inter-node distance

11564-
9251-
6938-
4626-
2313-

9 10 11 12 13 14 15 16 17 18 19+
Mean distance
 Number of nodes 



20 most tightly coupled nodes.
Below are the MathTree nodes with shortest mean distance.

Rank Mean dist Name Institution Area Date
1 9.29 Gregory C. Langmead (Info) Columbia University physical chemistry 2015-11-07
2 9.29 Pedram Safari (Info) Columbia University physical chemistry 2015-11-07
3 9.29 Adrian Clingher (Info) Columbia University physical chemistry 2015-11-07
4 9.29 Mehrzad Ajoodanian (Info) Columbia University physical chemistry 2015-11-07
5 9.29 Brendan E. Owens (Info) University of Glasgow physical chemistry 2015-11-07
6 9.47 Ruojia Li (Info) University of Wisconsin, Madison 2015-11-30
7 9.47 Wenqing Lu (Info) University of Wisconsin, Madison 2015-11-30
8 9.47 Li-Fei Huang (Info) University of Wisconsin, Madison 2015-11-30
9 11.05 George F. Carrier (Info) Brown University modeling of fluid mechanics, combustion, and tsunamis 2013-09-11
10 12.08 Tony Perkins (Info) Syracuse University Compact sets 2015-11-13
11 12.5 Eliakim Hastings Moore (Info) University of Chicago 2011-05-30
12 14.58 William T. Freeman (Info) Massachusetts Institute of Technology Computer vision 2008-06-22
13 15.09 Rudolph Ernest Langer (Info) University of Wisconsin, Madison 2012-02-27
14 15.43 Hugh Lonsdale Turrittin (Info) University of Minnesota, Twin Cities 2012-02-27
15 16 Eric Lander (Info) Broad Institute Human genome 2010-12-27
16 16.06 Jacques-Louis Lions (Info) Collège de France Partial differential equations 2011-06-18
17 17.35 Leonhard Euler (Info) Royal Prussian Society of Sciences mathematics 2009-05-28
18 17.66 Francesco Severi (Info) University of Rome 2007-01-26
19 17.77 Laurent Schwartz (Info) Université Paris Diderot - Paris 7 2007-10-17
20 17.81 Johann Bernoulli (Info) Universität Basel 2009-08-27


Distribution of individual connectivity.
Another way to look at the MathTree graph is to plot a histogram of researchers (nodes) based according to the number of immediate connections (edges) they have to other researchers. The final bin includes nodes with 16 or more connections. The actual distribution has a very long tail, with a maximum of 95 connections. Thanks to Adam Snyder for suggesting this analysis!

Edge vs node distribution

27909-
22327-
16745-
11164-
5582-

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16+
Number of connections
 Node count