×

Network analysis of Zentralblatt MATH data. (English) Zbl 1305.01052

Summary: We analyze the data about works (papers, books) from the time period 1990–2010 that are collected in Zentralblatt MATH database. The data were converted into four 2-mode networks (works \(\times\) authors, works \(\times \) journals, works \(\times\) keywords and works \(\times\) mathematical subject classifications) and into a partition of works by publication year. The networks were analyzed using Pajek – a program for analysis and visualization of large networks. We explore the distributions of some properties of works and the collaborations among mathematicians. We also take a closer look at the characteristics of the field of graph theory as were realized with the publications.

MSC:

01A90 Bibliographic studies
91D30 Social networks; opinion dynamics
68R10 Graph theory (including graph drawing) in computer science

Software:

FCMappers; plfit; Pajek
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Ajiferuke, I., Burell, Q., & Tague, J. (1988). Collaborative coefficient: A single measure of the degree of collaboration in research. Scientometrics, 14(5–6), 421–433. doi: 10.1007/BF02017100 . · doi:10.1007/BF02017100
[2] Batagelj, V., & Cerinšek, M. (2013). On bibliographic networks. Scientometrics, 96(3), 845–864. doi: 10.1007/s11192-012-0940-1 . · doi:10.1007/s11192-012-0940-1
[3] Batagelj, V., Doreian, P., Ferligoj, A., & Kejžar, N. (2014). Understanding large temporal networks and spatial networks: Exploration, pattern searching, visualization and network evolution. New York: Wiley.
[4] Batagelj, V. & Mrvar, A. (2014). Pajek and Pajek-XXL - Program for analysis and visualization of large networks. http://mrvar.fdv.uni-lj.si/pajek/pajekman. Accessed 7 May 2014. · Zbl 1054.68564
[5] Batagelj, V., & Zaveršnik, M. (2011). Fast algorithms for determining (generalized) core groups in social networks. Advances in Data Analysis and Classification, 5(2), 129–145. doi: 10.1007/s11634-010-0079-y . · Zbl 1284.05252 · doi:10.1007/s11634-010-0079-y
[6] Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703. doi: 10.1137/070710111 . · Zbl 1176.62001 · doi:10.1137/070710111
[7] De Nooy, W., Mrvar, A., & Batagelj, V. (2012). Exploratory social network analysis with Pajek (structural analysis in the social sciences) (2nd ed.). Cambridge; New York: Cambridge University Press.
[8] Garfield, E. (1979). Citation indexing: Its theory and application in science, technology, and humanities. New York: Wiley.
[9] Grcar, J. F. (2010). Topical bias in generalist mathematics journals. Notices of the AMS, 57(11), 1421–1424. · Zbl 1220.00029
[10] De Solla Price, D., de Beaver, D., & B., (1966). Collaboration in an invisible college. American Psychologist, 21(11), 1011–1018.
[11] Robertson, S. (2004). Understanding inverse document frequency: On theoretical arguments for IDF. Journal of Documentation, 60(5), 503–520. doi: 10.1108/00220410410560582 . · doi:10.1108/00220410410560582
[12] TePaske-King, P. & Richert, N. (2001). Database reviews and reports. The identification of authors in the mathematical reviews database. http://www.istl.org/01-summer/databases.html. Accessed 7 May 2014.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.