  In this article we find exponential good approximation of the empirical
neigbourhood distribution of symbolled 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 also show that the LDP
for the empirical degree measure of the classical Erd\H{o}s-R\'{e}nyi 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\H{o}s-R\'{e}nyi graph.
