Critical thresholds for scale-free networks against cascading failures

We explore the critical thresholds of scale-free networks against cascading failures with a tunable load redistribution model which can tune the load redistribution range and heterogeneity of the broken node. Research suggests that the critical behavior belongs to the universality class of global load preferential sharing rule (GLPSR) and local load preferential sharing rule (LLPSR) in networks. Networks collapse completely when α<αc1 and are immune to single failure when α>αc2. The changing trends for the critical thresholds of αc1 and αc2 are in an opposite way with initial load distribution coefficient and redistribution heterogeneity coefficient. It means networks may show different properties in the middle ground between total robustness and total collapse. Another striking finding is that the decrease of the exponent γ(γ>1) of scale-free networks would make the system stronger against cascading failure within LLPSR and GLPSR.