Models of Random Graphs

In this survey talk I will discuss several, old and new, models of random graphs. The main aim of the talk is to familiarize the audience with the variety of models of random graphs, while stressing their differences and similarities and emphasizing common research approaches and methodology. Between the models I plan (or rather hope) to discuss are:

• binomial random graphs G(n,p) and the Erdos-Renyi model G(n,m);
• graph processes and hitting times;
• random regular graphs;
• network reliability model;
• adding random edges (smoothed analysis);
• random lifts;
• preferential attachment models.

Although no previous research experience with random graphs will be assumed, a genuine interest in the subject would be appreciated.