Detecting the core network of microblog using snowball sampling

According to the influence oflline or online, some people, who are superstars, have many followers and possess dominant positions in the networks. They form the core of the networks, which controls the information flow in the complex systems. Different with other social network services, users in microblog are connected by directed and asymmetric relations. The users can follow any others as they liked. In practice, with many technical and privacy restrictions, collecting superstars' information and acquiring representative network samples is a big challenge for studying the critical structures of a large directed network. The paper studies the effectiveness of snowball sampling in recovering the core nodes in directed networks. We constructed a network of 35 million users of the most influential microblog in China-Sina Weibo. The snowball sampling with various strategies of choosing sampling seeds, waves, and branches performed well. The results reveal the systematic biases of different sampling schemes. Although snowball sampling with a few seeds and waves can cover most of superstars in the network, their indegree distribution is significantly affected by the sample dependency, which is introduced by the sampling strategies.