Seminar: Random graphs

Winter semester 2021/22

Prof. Dr. Silke Rolles

• Time and place: weekly, time and place to be announced
• First talk: during the first week of lectures
• Prerequisites: Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009).
• Content: Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.
• Literature:
  • R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017). Homepage of the book 
  • Manfred Lehn: Wie halte ich einen Seminarvortrag 
• Bachelor or Master thesis: It is possible to write a Bachelor or Master thesis on a related topic.
• Talks: Every talk is based on parts of a chapter of the book by Remco van der Hofstad.
  1. 1.1-1.7 Introduction
  2. 1.8-1.9 Introduction, 2.1-2.3 Probabilistic Method
  3. 2.4-2.6 Probabilistic Method
  4. 3.1-3.4 Branching Processes
  5. 3.5-3.7 Branching Processes
  6. Phase transition for the Erdös-Renyi random graph, part 1
  7. Phase transition for the Erdös-Renyi random graph, part 2
  8. 5.1-5.2 Erdös-Renyi random graph revisited
  9. 5.3-5.4 Erdös-Renyi random graph, Intermezzo: Back to real-world networks
  10. 6.1-6.4 Generalized random graphs
  11. 6.5-6.8 Generalized random graphs
  12. 8.1-8.5 Preferential attachment models