关键词: 复杂网络, 节点重要性排序, 多层次灰色关联分析, 修正的聚类系数, Erdos数, 介数

Abstract:

Nodes importance ranking in complex network is one of the most important aspects of studying the properties of complex network. It has been widely used in data mining, web search, analysis of social network and so on. When selecting the node importance evaluation index, considering that the average clustering coefficient can only measure a network node clustering density, and not measure the clustering size, the amended clustering coefficient is proposed. Meanwhile, the other two indexes, the Erdos number and the betweenness,are selected to evaluate node importance in networks. A multilevel gray relational analysis model is established to identify the correlation degree between node and the optimal node,and to sort nodes of complex networks. The model considers the node sorting influence factors involving not only the degree of nodes and the path distance but also the degree of node clustering.Compared with the real network and other methods of sorting results,the model can accurately find the core nodes of the complex network,and the sorted results truly reflect the important degree of nodes.

Key words: complex network;nodes importance ranking;multilevel gray relational analysis;amended clustering coefficient;Erdos number;betweenness