Formation of circulation in complex networks

We study the mechanism that forms the cyclic topology in various scale-free networks. An evolving network model is introduced in which the ratio of the number of edges attaching a new vertex to old vertices and that linking between old vertices is controlled and the edges are attached in three different ways with probability parameters. By controlling the ratio and the probability parameters, we realize model networks showing almost the same cyclic topology as that of various real networks. This indicates that the cyclic property of each network is determined by the ratio of the tree-like structure, triangular structure, and quadrangular structure.