改进的加权网络节点重要性评估的互信息方法

Improved evaluation method for node importance based on mutual information in weighted networks

现有的复杂网络节点重要性评估研究主要集中在无向无权网络上,不能全面客观反映某些真实复杂网络的情况。针对无向加权和有向加权网络中评估指标适用范围有限、评估结果不够全面等问题,借鉴应用于无向无权网络的基于互信息的节点重要性评估方法,提出适用于无向加权网络和有向加权网络的互信息评估方法。该方法将网络中的每条边看作信息流,结合相应复杂网络的结构特点和"信息量"的定义方法,以求出的节点信息量作为节点的重要性评估指标。对实例网络进行分析可知,所提算法在保证评估准确性前提下,能更加细致刻画有向加权网络节点之间的差异性。在对ARPA网络的节点评估中,所提算法与以往指标所评估出的前5个最重要节点的节点编号尤其相近,凸显出该算法快速发掘核心节点的能力,为快速、准确评估无向加权和有向加权网络核心节点,提高网络抗毁性提供一定理论帮助。

The existing evaluation methods for node importance in complex network mainly focus on undirected- unweighted complex networks, and can not reflect objectively the reality of some real world status. Focusing on the problems such as the limited scope of evaluation indexes and not enough comprehensive evaluation results in the undirected-weighted and directed-weighted networks, and the node importance evaluation method in undirected-unweighted networks based on mutual information was used for reference, a new evaluation method based on mutual information that is suitable for the undirected- weighted and directed-weighted networks was proposed. In this method, each edge was regarded as a flow of information, the structure characteristics of the corresponding complex networks and the definition method of ＂amount of information＂ were considered, then the amount of information was calculated as the node importance evaluation index. The analyses of the instance network show that the proposed algorithm can more detailed describe the differences between nodes in the directed- weighted network under the premise of guaranteeing estimation accuracy. In the evaluation of the ARPA （ Advanced Research Project Agency） network nodes, the first five most important nodes number that were evaluated from the proposed algorithm and the previous indexes were especially close, so the algorithm＇s ability of finding the core nodes was highlighted. The proposed algorithm provides a certain theoretical help for evaluating the core nodes in the undirected-weighted and directed- weighted networks and improving the network invulnerability ability quickly and accurately.