The Measurement of Sparseness and Denseness of Scale-Free Networks Based on Controllability

Abstract

How to quantitatively analysis the sparseness and denseness of scale-free networks has not been well solved. In studying the structural controllability of BA scale-free networks, we find that for a BA scale-free network with fixed number of nodes, if it has more edges, it will be more structural controllable. And to a BA scale-free network with N nodes, if it has more than 5N edges, it can still controllable under random failures. We then say that a BA scale-free network with N nodes and more than 5N edges is a dense network in the sense of controllability, if not, we say it is a sparse network.