Abstract
Minimum driver node sets (MDSs) play an important role in studying the structural controllability of complex networks. Recent research has shown that MDSs tend to avoid high-degree nodes. However, this observation is based on the analysis of a small number of MDSs, because enumerating all of the MDSs of a network is a #P problem. Therefore, past research has not been sufficient to arrive at a convincing conclusion. In this paper, first, we propose a preferential matching algorithm to find MDSs that have a specific degree property. Then, we show that the MDSs obtained by preferential matching can be composed of high- and medium-degree nodes. Moreover, the experimental results also show that the average degree of the MDSs of some networks tends to be greater than that of the overall network, even when the MDSs are obtained using previous research method. Further analysis shows that whether the driver nodes tend to be high-degree nodes or not is closely related to the edge direction of the network.
Highlights
Controlling complex systems is a critical topic in many applications
Previous researches have usually adopted a complex network as the fundamental model to analyze the topological structure [1,2,3], the evolving model [4,5,6], and the dynamic behavior [7,8,9] of complex systems
We propose a preferential matching algorithm to find some minimum driver nodes sets (MDSs) with desired degree properties
Summary
Controlling complex systems is a critical topic in many applications. A system is called controllable if it can be driven from any initial state to any desired state in a finite time. Liu [13] developed an analysis tool to study the controllability of an arbitrary complex directed network, and found that MDSs tend to be composed of low-degree nodes in both real and model networks. Because low-ranking nodes have higher probabilities of being driver nodes, the obtained MDSs tend to be composed of the high- or the medium-degree nodes of the network.
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