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|
|Number of nodes|
20 most tightly coupled nodes.
Below are the MathTree nodes with shortest mean distance.
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|
|Number of connections|