Node-importance ranking in scale-free networks: a network metric response model and its solution algorithm

A new node-importance ranking model and its solution algorithm for scale-free networks are proposed. The general idea is as follows: first, we construct a node-importance ranking model targeting the fastest network collapse, which is identified by the maximal variation in integrated network metrics. We then combine the genetic algorithm and variable neighbourhood search and improve it in initial population generation, neighbourhood search, and fitness evaluation. Finally, we investigate the BA network and container-shipping network. By comparison, the proposed method demonstrates a 7.9 and 16.8% improvement in effectiveness over betweenness and degree, respectively, in the BA network. The above indexes come to 15.1 and 41.3% in the container-shipping network. Moreover, the proposed algorithm reveals an 8.1 and 6.3% improvement in effectiveness, and a 63.7 and 67.1% reduction in computation time in the two cases, respectively. The research sheds new lights on not only analytical methods of complex theory but also practical application.