Local Large deviations for empirical locality measure of typed Random Graph Models

Abstract. In this article, we prove a local large deviation principle (LLDP) for the empirical locality measure of typed random networks on n nodes conditioned to have a given empirical type measure and empirical link measure. From the LLDP, we deduce a full large deviation principle for the typed random graph, and the classical Erdos-Renyi graphs, where nc/2 links are inserted at random among n nodes. No topological restrictions are required for these results.