Statistical network analysis for collaboration in applied mathematics

Güneri, Simge
In spite of easy access to academic information, person-to-person contact is still signi ficant so as to provide the academic issues to be discussed in more detail and well-developed. So, throughout the thesis, we investigate one-to-one communication and frequency of activities performed together in the researcher communities from di fferent study fields of applied mathematics. We deal with this problem by taking each researcher community as a network where its entities are considered the researchers and two entities are connected if the two reseachers published an article together. The underlying data were derived from the archives of ArXiv. Firstly, we apply the statistical procedure based on the hypothesis test to model our collaboration networks. By use of the technique combining both maximum likelihood estimation method and Kolmogorov-Smirnov statistic, we investigate the cumulative distribution of its degree sequence for each network which gives the probability of total collaborators of an arbitrarily chosen mathematician being greater than or equal to a speci fied number. Secondly, we evaluate mean number of collaborators of the researchers, mean size of small groups of connected researchers, size of a giant assemble of connected researchers, mean shortest distance and maximum shortest distance between the researchers in the giant assemble both empirically and theoretically. In addition, we also calculate the degrees of clustering and mutuality, indicative properties of real networks. Finally, as observed in most real networks, we see that relationships on almost all communities show a small-world e ffect which is an indication of small mean distance and high clustering. However, the communities are not scale free. Beside scienti fic collaboration networks, we can also use our findings to make an analysis of the other types of networks such as gene regularity networks and social media networks.


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Citation Formats
S. Güneri, “Statistical network analysis for collaboration in applied mathematics,” M.S. - Master of Science, Middle East Technical University, 2013.