**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Introduction: Background from probability theory, convergence of random variables, concentration inequalities, Markov chains, martingales.
- Fundamental Random Graph Models: Random Binomial Graphs (also known as Erdos-Renyi graphs), Uniform Random Graph, Geometric Random graphs.
- Branching Processes: Survival and Extinction, Total Progeny, Subcritical and Supercritical Branching process, Binomial and Poisson Branching Processes.
- Phase Transition in Random Graphs: Phase transition of Erdos-Renyi graphs of degree smaller than 1, Phase transition for degree larger than 1, giant connected components.
- Small-World Networks and Preferential Attachment Models: Degree sequences, degree sequences of real-world networks.

- Stochastic Processes on Random Graphs.

- B. Bollobas, Random Graphs, 2 Edition, Cambridge University Press, 2001.
- M. Penrose: Random Geometric Graphs, Oxford University Press, 2003.
- A. Frieze and M. Karonski, Introduction to Random Graphs, Cambridge University Press, 2015.
- S. Janson, T. Luczak and A. Rucinski, Random Graphs, Wiley 2000.