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

Published online by Cambridge University Press:  10 October 2014

FLAVIO B. GONZAGA,
VALMIR C. BARBOSA and
GERALDO B. XEXÉO
FLAVIO B. GONZAGA
Affiliation:
Núcleo de Ciência da Computação, Universidade Federal de Alfenas, 37130-000 Alfenas - MG, Brazil (e-mail: fbgonzaga@bcc.unifal-mg.edu.br)
VALMIR C. BARBOSA
Affiliation:
Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21941-972 Rio de Janeiro - RJ, Brazil (e-mail: valmir@cos.ufrj.br, xexeo@cos.ufrj.br)
GERALDO B. XEXÉO
Affiliation:
Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21941-972 Rio de Janeiro - RJ, Brazil (e-mail: valmir@cos.ufrj.br, xexeo@cos.ufrj.br)
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Abstract

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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.

Keywords

online mathematical librariesWikipediaMathWorldDLMFcomplex networkstext search

Information

Type
Research Article
Information
Network Science , Volume 2 , Issue 3 , December 2014, pp. 367 - 386
Copyright
Copyright © Cambridge University Press 2014 

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