Evaluating the importance of nodes in complex networks based on principal component analysis and grey relational analysis

A central challenge for the complex network analysis is how to identify key nodes. Although there are many evaluation methods, most of them use single-criteria (degree or shortest path), which is often confronted with the problem of incomplete information on the structure of the complex network. Different criteria often lead to significantly different results. Therefore, this paper proposes a multi-criteria evaluating method (PCGRAE) based on principal component analysis (PCA) and grey relational analysis (GRA) specifically. PCA is applied to confirm the weight for evaluating criteria, GRA is used to calculate the importance of node, and a novel measure of complex network robustness is presented to assess the accuracy of PCGRAE. According to the evaluation results with simulated and real networks, PCGRAE has good performance on discrimination and precision to evaluate the importance of nodes.