Research on centrality of node importance in scale-free complex networks

It is a basic issue to assess each node importance in complex networks. Many algorithms are developed to research centralities, for instance degree, betweenness, closeness, eigenvector and eccentricity, which are from different angles. However the relationships among different centrality are not paid enough attention. In this paper, we try to explore the relationships of multiple centralities with factor analysis. The BA networks with number of nodes arrange from 5000 to 10000 and a true network - Internet are excavated. Experiment results show that the widely used five centralities in scale-free complex networks are divided to two classes: 1) degree, betweenness and eigenvector that mainly reflect the node influences with others; 2) closeness and eccentricity related to network topology. Furthermore these analysis results can be used in the objective and accurate assessment of node importance.