Doku-Amponsah, K2015-06-232017-10-142015-06-232017-10-142014http://197.255.68.203/handle/123456789/6249In this article we find exponential good approximation of the empirical neigbourhood distribution ofsymbolled random graphs conditioned to a given empirical symbol distribution and empirical pair distribution.Using this approximation we shorten or simplify the proof of (Doku-Amponsah and Morters 2010, Theorem 2.5);the large deviation principle (LDP) for empirical neigbourhood distribution of symbolled random graphs. We alsoshow that the LDP for the empirical degree measure of the classical Erd˝os-R´enyi graph is a special case of (Doku-Amponsah and Moerters, 2010, Theorem 2.5). From the LDP for the empirical degree measure, we derive an LDP for the the proportion of isolated vertices in the classical Erd˝os-R´enyi graph.concentration inequalitiescouplingempirical occupancy measureempirical degree measuresparse random graphsbins and ballsArticle