On the scale-free intersection graphs

In this paper we study a network model called scale-free intersection graphs, in which there are two types of vertices, terminal vertices and hinge vertices. Each terminal vertex selects some hinge vertices to link, according to their attractions, and two terminal vertices are connected if their selections intersect each other. We obtain analytically the relation between the vertices attractions and the degree distribution of the terminal vertices and numerical results agree with it well. We demonstrated that the degree distribution of terminal vertices are decided only by the attractions decay of the terminal vertices. In addition, a real world scale-free intersection graphs, BBS discussing networks is considered. We study its dynamic mechanism and obtain its degree distribution based on the former results of scale-free intersection graphs.