A new bound in information theory

Shannon Entropy, for discrete-valued random variables, plays important roles in information theory [1], especially for the transmission, processing and storage of information and also in measure theory with major impact to data integration and probabilistic estimation. The purpose of this paper is to present a new bound for the Shannon Entropy, by first developing a refinement of Jensen's inequality. This refinement is applied in order to find a new and more accurate upper bound for Shannon Entropy. Based on this, the paper presents an application to structural complexity analysis of a computer network modeled by a connected graph.