Thesis supervisor: István Fazekas
Location of studies (in Hungarian): University of Debrecen Faculty of Informatics Abbreviation of location of studies: DE IK
Description of the research topic:
Syllabus
Foundation an applications of network theory. Random graphs as models of networks. Finding new random graph models. Studying the interaction of various graph evolution methods (uniform, preferential attachment,…). Obtaining new properties of existing random graph models. Evolution of random graphs. Asymptotic properties of random graphs. Clusters, diameter, giant component, scale-free property, small word. Processes on graphs. Mathematical tools: branching processes, martingales. Computer simulations. Applications.
Bibliography
Durrett, R.: Random graph dynamics. Cambridge University Press, Cambridge, 2010.
Barabási, Albert-László: Network science. Cambridge University Press, 2018.
Bollobás, B.: Random graphs. Cambridge University Press, Cambridge, 2001.
Fazekas, I., Noszály, Cs., Perecsényi, A.: A population evolution model and its applications to random networks.
Statistics & Probability Letters 143, 17-27, 2017.
Fazekas I., Porvázsnyik B.: Limit theorems for the weights and the degrees in an N-interactions random graph model, Open Mathematics 14: (1) pp. 414-424, 2016.
Janson, S.; Łuczak, T.; Rucinski, A.: Random graphs. Wiley-Interscience, New York, 2000.
R. van der Hofstad. Random Graphs and Complex Networks. Vol. 1. Cambridge Series in Statistical and Probabilistic Mathematics, 2017.
R. van der Hofstad: Random Graphs and Complex Networks. Vol 2. Eindhoven University of Technology, 2017.
Móri, T.F.: Degree distribution nearby the origin of a preferential attachment graph. Elect. Comm. in Probab. 12 (2007), 276-282.
Deadline for application: 2019-11-15
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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