CASCADING FAILURES IN BARABÁSI–ALBERT SCALE-FREE NETWORKS WITH A BREAKDOWN PROBABILITY

Abstract

In this paper, adopting the initial load of a node j to be [Formula: see text], where kj is the degree of the node j and α is a tunable parameter that controls the strength of the initial load of a node, we propose a cascading model with a breakdown probability and explore cascading failures on a typical network, i.e., the Barabási–Albert (BA) network with scale-free property. Assume that a failed node leads only to a redistribution of the load passing through it to its neighboring nodes. According to the simulation results, we find that BA networks reach the strongest robustness level against cascading failures when α = 1 and the robustness of networks has a positive correlation with the average degree 〈k〉, not relating to the different breakdown probabilities. In addition, it is found that the robustness against cascading failures has an inversely proportional relationship with the breakdown probability of an overload node. Finally, the numerical simulations are verified by the theoretical analysis.