Structure controllability of complex network based on preferential matching

TL;DR

This paper introduces a preferential matching algorithm to analyze the degree properties of minimum driver node sets in complex networks, revealing their composition and relation to network edge directions.

Contribution

It proposes a novel preferential matching method for finding MDSs with specific degree properties and analyzes their composition and relation to network edge directions.

Findings

MDSs can include high- and medium-degree nodes.

Average degree of MDSs can be higher than the network's average.

Edge direction influences whether driver nodes are high-degree nodes.

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.