Factors That Affect the Centrality Controllability of Scale-Free Networks**Supported by Foundations of SiChuan Educational Committee under Grant No 13ZB0198, the National Natural Science Foundation of China under Grant Nos 61104224, 81373531, 61104143 and 61573107, and The Science and Technology Fund Project of SWPU (2013XJR011).

Abstract

The influence of a node in a network can be characterized by its macroscopic properties such as eigenvector centrality. An issue of significant theoretical and practical interest is to modify the influence or roles of the nodes in a network, and recent advances indicate that this can be achieved by just controlling a subset of nodes: the so-called controllers. However, the relationship between the structural properties of a network and its controllability, e.g., the control of node importance, is still not well understood. Here we systematically explore this relationship by constructing scale-free networks with a fixed degree sequence and tunable network characteristics. We calculate the relative size (nC*) of the minimal controlling set required to control the importance of each individual node in a network. It is found that while clustering has no significant impact on nC*, changes in degree–degree correlations, heterogeneity and the average degree of networks demonstrate a discernible impact on its controllability.