ABSTRACT
In this chapter, we first introduce the asymptotic notation that we will use. Next, we introduce the binomial random graph model and closely related models. Unfortunately, many real-world networks exhibit different degree distributions than the one produced by these models, so one needs to generalize them to allow for more flexibility—the Chung-Lu model provides it. However, this model generates a random graph with only the expected degree distribution matching the desired one. The next two models generate random graphs whose degree distribution is an exact match for what we prescribe. We start with random d-regular graphs and then generalize the model to any degree distribution. Several examples are provided for all those models.
