Universal Scaling Behavior of Clustering Coefficient Induced by Deactivation Mechanism

TL;DR

This paper introduces a generalized network growth model demonstrating that the clustering coefficient scales inversely with the number of active nodes, revealing a universal behavior driven by the deactivation mechanism.

Contribution

The study analytically and through simulations shows that the clustering coefficient's inverse scaling with active nodes is a universal property of deactivation-based network models.

Findings

Clustering coefficient scales as 1/M with active nodes.

Deactivation mechanism explains clustering behavior in real networks.

Scaling law persists under network perturbations.

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.