A new approach for node centrality evaluation based on residual network performance measurement

Abstract

SummaryThe identification of the most influential nodes has been a vibrant subject in complex network research, with many applications across informational, social or biological networks. Despite substantial empirical studies, there is still some defect in the traditional approach for evaluating nodes centralities. The traditional approach for evaluating nodes centralities is to measure network performance change before and after a node fails. To be compatible with this approach, network performance measurement indexes should be monotonic and adequate, which is a constraint condition too strong to satisfy. As a result, many indexes were actually abused in some topologies of networks and the ranking result of nodes centralities may be unreasonable in some application scenarios. To solve the problem, the fundamental rationale of this approach is studied as well as its theoretical defect. Then, a new approach is proposed for evaluating node centrality based on measurement of residual network performance after a node fails. Furthermore, a new index called comprehensive distance is presented for measuring network interconnectedness whether cascading failure is considered or not, which is suitable for not only connected networks but also unconnected networks. Finally, some cases are used to test the validity of the proposed approach. By comparison, the ranking results of nodes centralities evaluated by the proposed approach are more accurate than the results evaluated by the traditional approach. The study about how to measure performance of residual network not only advances the field in terms of node centrality evaluation but also promotes the state of the art in recent related fields such as neural network research and application.