Resources

To visualize networks from your own data, use the original browser tool this site modified from, Network Navigator:

The data for the networks generated by this website comes from Microsoft Academic Graph, a database containing scientific research citation relationships between algorithmically-generated fields of study. Machine-created fields are often nonsensical, so we hand-selected which fields to include in our networks through our subjective filters of sensibility, as well as what we deem too general or specific.

We are interested in investigating which fields of study in math research are most important from year to year. This browser tool calculates some mathematically-defined measures of importance called centrality measures, defined below in the context of our research:

Degree Centrality: The degree centrality of a field of study is the count of edges leaving and arriving at that node.

Eigenvector Centrality: The eigenvector centrality of a field of study is like its weighted degree centrality, in that the connections of that field to important fields are given more weight in the summation. Exactly how much weight is determined by the eigenvalues and eigenvectors of the matrix-representation of a network. In short, eigenvector centrality acknowledges that some connections are more valuable than others. A field connected to a few important fields may have a similar eigenvector centrality to a field connected to many unimportant ones.

Betweenness Centrality: The betweenness centrality of a field of study is the fraction of shortest paths between all other nodes that that field of study lies on over total paths between all nodes.

Last Updated: April 2022