Bayesian optimization algorithm is very important a type of the intelligent optimization algorithms. It uses Bayesian networks to model promising solutions from the current population and has proven to optimize problems of bounded difficulty quickly, reliably,and accurately. However,learning the structure of a Bayesian network from data is a difficult problem, and it also needs consuming mass computational resources.This paper is focus on theoretical analysis about local network structures based-on Bayesian Dirichlet metric. Several results about the local metric relation of Bayesian networks are obtained in the paper. They are very important not only for constructing a Bayesian networks fitting a given dataset, but also for machine learning and data mining.