基于随机匹配的复杂网络最小驱动点集分析

Analysis of minimum driver node set of complex network based on random matching

控制复杂网络在很多领域都有着重要的应用价值.将控制复杂网络所需的最少节点集合称为最小驱动点集.针对网络的最小驱动点集并不唯一,提出一种随机匹配方法来获取网络中不同的最小驱动点集,并分析最小驱动点集集合的平均度分布以及节点在最小驱动点集集合中的出现频率.研究发现,多数网络的最小驱动点集分布紧密,其节点构成与网络度分布有关;同时,网络中节点的控制重要性与其入度密切相关.所得到的相关结论对于复杂网络的控制具有重要的研究意义.

Controllability of complex networks has important application value in many areas. The minimum driver node set is defined as the minimum nodes required to the control complex network. However, the minimum driver node set of most of network is not unique. Therefore, a random matching method is proposed to obtain different minimum driver node set of a network. Then, the method analyzes the average degree distribution of the collection of minimum driver node sets, and the frequency appears in the collection of the node. It is found that the minimum driver node sets of most networks are distributed tightly. The composition of a driver node set is closely related with the degree distribution of network. The control importance of the node in a network is closely related to the in-degree of node. These conclusions have important research meaning for the controllability of the complex network.