Large Networks & Random Graphs - Interaktive Studienpläne der TU Ilmenau

Stochastics (e.g. Diskrete Stochastik (200401) or Stochastik (200375),
Discrete Mathematics (e.g. Graphen & Algorithmen (200408))

Students are familiar with various models of random graphs, their potential applications as well as advantages and disadvantages. They can select a suitable model for an application problem, examine it methodologically and apply and develop algorithms for it. They are also able to read current literature in the context of scientific research at the time. They can present the results and conclusions and are able to discuss and reflect them.

Models of random graphs G(n,p), G(n,m), G(n,d) and their most important properties. Thresholds and expectation thresholds. Random geometric graphs and models for complex networks. Algorithms on random graphs.

Moodle, slides or PC presentations, blackboard and worksheets

B. Bollobás: Random Graphs, 2nd edition; Cambridge University Press, 2001.
A. Frieze, M. Karonski: Introduction to Random Graphs; Cambridge University Press, 2015.
A. Frieze, M. Karonski: Random Graphs and Networks: A First Course; Cambridge University Press, 2023.
S. Janson, T. Luczak, A. Rucinski: Random Graphs; Wiley, 2000.
Research papers.

Person, Yury