C284r: Social Data Mining Lecture 1: Random Graphs

Formally, when we are given a graph G and we say this is a random graph, we are wrong. A given graph is fixed, there is nothing random to it. What we mean though through this term abuse is that this graph was sampled out of a set of graphs according to a probability distribution. For instance, Figure 1.1 shows the three possible graphs on vertex set [3] = {1, 2, 3} with 2 edges. The probability distribution is the uniform, namely, each graph has the same probability 13 to be sampled.