Invulnerability of scale-free network against critical node failures based on a renewed cascading failure model

• The invulnerability of scale-free network against cascading failures is investigated based on a renewed cascading model.
• There is a threshold αTαT that the High-loads-attacking strategy will make more or less damage for the scale-free network when the loads distribution index αα is above or below αTαT.
• For BA scale-free network, the threshold αTαT is approximately 0.6, this conclusion is got through numerical simulation and theoretical analyses.

The invulnerability or robustness of complex networks against cascading failures under critical node failures is of great realistic meaning. Inspired by other related works, we propose a renewed cascading failure model which should be more suitable for real networks. In this model, the initial node loads are defined as a nonlinear function of the generalized betweenness with a power exponent αα, and the local distribution strategy is adopted to assign the failed nodes’ loads to their neighbors. In frame of the BA network, an interesting conclusion is reached through numerical simulations: there is a threshold αT≈0.6αT≈0.6, in the case of α>αTα>αT, attacking the nodes with larger loads is more prone to large scale cascading failures; while for α<αTα<αT, attacking the nodes with smaller loads will more easily lead to the whole network’s paralysis. Finally, we indicate that this phenomenon is rooted in the differences of initial loads distribution for different values of αα.