Identification of cascading dynamic critical nodes in complex networks

Catastrophic events occur frequently on the internet and power grids as well as other infrastructure systems in recent years, which can be considered, to some extent, to be triggered by minor events. To study the dynamic behaviour on these systems, we generally should simplify them as networks. We should pay more attention to these backbone networks so as to explore the dynamic behaviour and mechanisms of the embedded systems more deeply and broadly. One of the major problems in the field of networks is how to identify the critical nodes. In this paper, we explore the identification method of cascading dynamic critical nodes in complex networks. By the average load oscillation extent of the affected nodes caused by attacking one node, we define the importance indicator of the attacked node with a cascading failure model based on a load preferential sharing rule. The indicator has two characteristics: one is that the failure consequence of the considered node can be clearly pointed out by its value. The other is that the evolution mechanism of node importance can be analysed with the factors of load redistribution mechanism, node capacity, and structural characteristics of the network. The experiments demonstrate the effectiveness and feasibility of the indicators and its algorithm, with which we also analyse the node importance evolution mechanism in-depth.