Abstract
In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology.
Highlights
In recent years, the study of complex networks has drawn the attention of many scholars from both the science and the engineering communities [1,2,3,4,5]
The controllability of complex networks is related to their network topology
A quantitative index is presented based on the control centrality and conditional number of the controllability matrix of controllable network system
Summary
The study of complex networks has drawn the attention of many scholars from both the science and the engineering communities [1,2,3,4,5]. Liu et al [18] addressed the structural controllability of arbitrary complex directed networks, identifying a minimal set of driver nodes that can guide the system to any desired state. They selected an index denoted by Nd to quantitatively measure the extent of controllability of complex networks. We will try to explore the possible ways to quantitatively measure the extent of controllability of any given network. It can be found that controllability of given network is related to their topologies, such as the number of nodes and edges and edge density, so it is possible to improve the controllability of the network by adjusting certain parameters, such as the connectivity probability p and the number of nodes N
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