Random Graph Model
A random graph model specifies a distribution on a set of graphs, modeling the Network generating process. A static random graph model specifies the distribution given a graph space, while a dynamic/growing random graph model specifies the distribution given the current graph and a new graph space. In other words, a static model can be thought of as having all nodes present at the same time and then having links drawn according to some probabilistic rule, while in a growing model, new nodes are introduced over time, and form links with existing nodes as they enter.