Cyclic Topology in Complex Networks

Abstract

We propose a cyclic coefficient $R$ which represents the cyclic characteristics of complex networks. If the network forms a perfect tree-like structure then $R$ becomes zero. The larger value of $R$ represents that the network is more cyclic. We measure the cyclic coefficients and the distributions of the local cyclic coefficient for both various real networks and the representative network models and characterize the cyclic structures of them.