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

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.

References in corpus (12)

• Emergence of scaling in random networks
• Error and attack tolerance of complex networks
• Power laws, Pareto distributions and Zipf's law
• Assortative mixing in networks
• The diameter of the world wide web
• Random graphs with arbitrary degree distributions and their applications
• Mixing patterns in networks
• Resilience of the Internet to random breakdowns
• Preferential attachment in the growth of social networks: the case of Wikipedia
• Giant strongly connected component of directed networks
• Edge direction and the structure of networks
• Wikipedias: Collaborative web-based encyclopedias as complex networks