A MODEL FOR CASCADING FAILURES IN COMPLEX NETWORKS WITH A TUNABLE PARAMETER

Abstract

In this paper, based on the local preferential redistribution rule of the load after removing a node, we propose a cascading model and explore cascading failures on four typical networks, i.e. the BA with scale-free property, the WS small-world network, the NW network and the ER random network. Assume that a failed node leads only to a redistribution of the load passing through it to its neighboring nodes. We find that all networks reach the strongest robustness level against cascading failures in the case of α=1, which is a tunable parameter in our model, where the robustness is quantified by the critical threshold Tc, at which a phase transition occurs from a normal state to collapse. To a constant network size, we further discuss the correlations between the average degree 〈k〉 and Tc, and draw the conclusion that Tc has a negative correlative with 〈k〉, i.e. the bigger the value of 〈k〉, the smaller the critical threshold Tc. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.