Multi-index evaluation algorithm based on principal component analysis for node importance in complex networks

The evaluation of vital nodes in complex networks has been an increasing widespread concern in recent years. Seeking and protecting vital nodes is important to ensure the security and stability of the whole network. Presently, most of the existing evaluation algorithms cannot completely reflect the circumstances of complex networks because these algorithms are proposed based on a certain characteristic of the network, and the single metric is incomplete and limited. With that said, the development of a new algorithm that evaluates node importance in complex networks is critical. First, a number of classic ranking measures for evaluating vital nodes have been demonstrated in the present study. Second, basic concepts of complex networks have been summarised further. Third, a new multi-index evaluation algorithm based on principal component analysis has been proposed. The algorithm can reveal the simple structure behind the complex data, and has no parameter restrictions to represent the features of the data. The algorithm presented in the current study synthesises the topological characteristics of the network, such as degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, mutual-information and local clustering coefficient to reflect the relative node importance. Finally, to verify the validity of the algorithm, a simulation experiment was conducted. The results indicated that the algorithm is more rational, effective, complete and accurate than the algorithm of single metric evaluation.