The influence of social network is closely related with its structural characteristics. Based on the data from Sina microblog, the distributions of the number of followers and followings were analyzed and found that the number of followers and followings both were power-law distributed. The distance characteristic between different pairs of nodes was discussed, and it was found and proved that there was "small-world" phenomenon in the microblog network. At last, the links between nodes in the network were investigated and found that the formation of the link satisfied triple closure principle. The investigation results on the above three topics are important for us to explore the relationship between the influence of micro-blog and the structural characteristics of its underlying social network, as well as to the design of mechanisms to control the influence.