The graph entropy $H(G,P)$ of a graph $G$ with probability distribution $P$ on its vertices was a concept introduced by János Körner in 1973 to solve the problem of source coding over an alphabet whose symbols are not all mutually distinguishable. We will outline the problem that Körner solved and survey some known results on graph entropy. A new lower bound on graph entropy will be proposed, and some applications discussed. In particular, this result allows the graph entropy of the odd cycles to be calculated under certain probability distributions.