Modul

The module will be completed by an oral exam (ca. 30 min). 

Students

• know the basic models of random graphs and their properties,
• are familiar with probabilistic techniques for the investigation of random graphs,
• are able to work in a self-organized and reflexive manner.

none

In the course, models of random graphs and networks are presented and methods will be developed which allow to state and prove results about the structure of such models.

In particular, the following models are treated:

• Erdös--Renyi graphs
• Configuration models
• Preferential-Attachment graphs
• Generalized inhomogeneous random graphs
• Geometric random graphs

and the following methods are addressed:

• Branching processes
• Coupling arguments
• Probabilistic bounds
• Martingales
• Local convergence of random graphs

The contents of the module 'Probability Theory' are strongly recommended.

Total workload: 240 hours

Attendance: 90 hours

• lectures, problem classes, and examination

Self-studies: 150 hours

• follow-up and deepening of the course content
• work on problem sheets
• literature study and internet research related to the course content
• preparation for the module exam.