I have been looking at the hiring networks in Mathematics (2015-02-18-math_phd_hiring_network_part_1.html) and here in the last two days. The resulting graphs are highly connected and difficult to read. In order to perform more flexible analyses and to simplify the workflow, I created another dataset which is easier to process, and I simplified the code that generates these graphs. You can find everything you need to play with the code and the data here.
The dataset now consists of person id, advisor’s school (name, country and id) and recipient’s school (name, country and id) and year of the degree. The code I wrote is bare bones. Depending on what you want, first you need to filter the data and then pipe it to the program. The command line parameters are
The weight function: first all PhD’s are counted for the filtered dataset. Then these numbers are normalized between 0 and 1. Then I apply the following function: w(x)=log(1+x) to the result up to a suitable scalar multiple and a cut off function.
Let us start looking at the graphs again:
France, The Netherlands and Germany (then Prussia) dominated the Math PhD network.
Hiring network between 1800 and 1910
The network has expanded, but the connections are not as strong as before. Germany still dominates, and we have new players appearing on the scene such as Russia and Ukraine. Also notice that both US and UK are importers of PhD degrees, and Germany is the main exporter. But this might be an inherent bias of the dataset. After all, Math Genealogy Project is based in the US.
Hiring network between 1910 and 1940
The number of PhD’s among Germany, The Netherlands, Austria and Switzerland expands. Russia starts exporting degrees to US. Also, notice the relationship between Germany and Spain, but we see no discernible relations between Germany and Italy in between two World Wars.
Hiring network between 1940 and 1985
Wow! Almost all PhD’s between 1940’s and 1980’s are given in the US. The US looks like this large sink that swallows all the math PhD’s. Also, notice that Russia’s influence expands. India now is visible, but not China.
Hiring network between 1985 and 2005
The US becomes the primary exporter of Math PhD’s. China shows up for the first time.
The US now dominating the scene. China appears on the horizon.
I will be looking at the specific network around the US, the UK and Canada.
Anglo-American Network Between 1800–1910
The Math PhD Network of the US is very small and largely depends on the UK and Germany.
Anglo-American Network Between 1910–1940
The network starts taking shape. The major hubs form: Chicago, Harvard, Urbana-Champaign, Johns Hopkins and Princeton.
Anglo-American Network Between 1940–1985
After US became the major importer of PhD degrees in math after the 2nd World War, major hubs form a tight network with some interesting subnetworks on the periphery: Texas Austin and small cluster of Southern Universities (not visible on this scale), New York University and its small network, Cambridge and its cross-continental subnetwork.
Anglo-American Network Between 1985–2005
I don’t know what it is but the PhD network became even more connected than previous eras. Increasing and decreasing the threshold doesn’t much change the structure of the graph. It is a highly connected graph with plenty of connections between the major hubs and the rest of the universities.
Anglo-American Network After 2005
The graph didn’t change much from the previous era.
