Directed acyclic graphs (DAGs) and completed partial directed acyclic graphs (CPDAG) are widely used to represent causal systems or uncertain probability systems.Some studies about small graphs with dozens of nodes have shown that given the number of nodes,p,in average,each CPDAG encode about 3.7 DAGs and few results are available about chain components in a CPDAG.In this paper,we will analyze the structure properties of CPDAGs with large dimensions and sparsity settings.We propose a Markov chain monte carlo approach to generate a sequence of CPDAGs.