Large deviation principles for empirical measures of the multitype random networks

In this article we study the stochastic block model also known as the multi-type random networks (MRNs). For the stochastic block model or the MRNs we define the empirical group measure, empirical cooperative measure and the empirical locality measure. We derive large deviation principles for the empirical measures in the weak topology. These results will form the basis of understanding asymptotics of the evolutionary and co-evolutionary processes on the stochastic block model.