Universal Scaling Behavior of Clustering Coefficient Induced by Deactivation Mechanism

Abstract

We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have been investigated analytically and by simulations. A scaling behavior of clustering coefficient $C \sim 1/M$ is theoretically obtained, where $M$ refers to the number of active nodes in the network. We discuss the relationship between the recently observed numerical behavior of clustering coefficient in the coauthor and paper citation networks and our theoretical result. It shows that both of them are induced by deactivation mechanism. By introducing a perturbation, the generated network undergoes a transition from large- to small-world, meanwhile the scaling behavior of $C$ is conserved. It indicates that $C \sim 1/M$ is a universal scaling behavior induced by deactivation mechanism.