复杂网络的影响可控性

Controlling Complex Networks via Influence

人们的行为受其他个体和连接彼此的社会网络的影响.研究基于影响网络的重要模型(DeGroot模型),在此模型中,社会网络可用一个加权的有向图表示,网络中的每个个体对某个共同的兴趣问题具有一个初始态度,由于网络中节点的相互影响而会逐步发生改变.提出一种框架用于分析复杂社会网络的影响可控性.结果表明,如果网络中存在持相反观点且对影响免疫的个体,群体对于命题的观点或态度可被固执的个体集合控制.通过分析网络完全影响可控或部分影响可控的条件,得到相应的可控准则.此外,提出控制影响网络的具体方法.由于网络的结构可控性已被广泛用于分析各种复杂网络,分析了网络的影响可控性与结构可控性的关系.

Human behavior is profoundly affected by individuals and the social network that links them together. We base our study on the important model of influence network largely due to DeGroot. In this model, the social structure of a society is described by a weighted and possibly directed network. Each node in the network takes an initial position about a common question of interest. At each date, nodes communicate with each other in the social network and update their positions because of the influences from neighbors. This paper presents a framework to analyze the controllability of social complex networks via influence. We show how the opinion, or attitude about some common questions can be controlled by a subset of committed nodes who consistently proselytize the opposing opinion and are immune to influence. Some controllable criteria are established to guarantee that a network can be fully or partially controllable. Besides, the methods to control an influence network are proposed. Because structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks in the physical and life sciences, the relationship between influence controllability and structural controllability of networks is also presented.