Structure learning of the Bayesian networks is a NP hard problem, and improving the efficiency of structure learning is one of the most important problems. The size of a searching space increases exponentially with the number of vertexes, and choosing and limiting the searching space of structure learning can improve the efficiency of a learning algorithm. This paper gives a qualitative and quantitive analysis on the searching space, compares the sizes and characteristics of the directed graph, the directed acyclic graph and the Markov equivalence class space. Based on the experiment data, we analyse the efficiency of constraining the prior structure space, and give an advice on choosing the parameters. These analyses are helpful when choosing the searching space and defining the parameters of constraints, thus  improving the efficiency of structure learning.