The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries

TL;DR

This study analyzes the network structure of mathematical content in Wikipedia, MathWorld, and DLMF, revealing unique features and suggesting new ways to search within these specialized online libraries.

Contribution

It provides a comparative network-theoretic analysis of three major mathematical online libraries, highlighting their structural similarities and differences.

Findings

Large strongly connected components in each library

Absence of clear power-law distributions in local features

Identification of stress centrality as effective for keyword search

Abstract

We study the network structure of Wikipedia (restricted to its mathematical portion), MathWorld, and DLMF. We approach these three online mathematical libraries from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web. We identify some distinguishing characteristics of all three libraries, most of them supposedly traceable to the libraries' shared nature of relating to a very specialized domain. Among these characteristics are the presence of a very large strongly connected component in each of the corresponding directed graphs, the complete absence of any clear power laws describing the distribution of local features, and the rise to prominence of some local features (e.g., stress centrality) that can be used to effectively search for keywords in the libraries.