Studies of Cascades of Overload Failure in Random Regular Networks

Abstract

We study the disintegration of a network when nodes fail due to a betweenness overload, triggered by an attack. We study the final size of the network as a function of the size of the attack. We look at different methods of finding the location and nature of the disintegration transition. We discuss the advantages and disadvantages of each method. We discuss a heuristic method to predict, based on the distribution of the nodes’ betweenness, what size attack will lead to the the network’s disintegration. We concentrate on the region where the network disintegrates through a series of cascades, and we detect interesting patterns in the number of cascade stages as a function of the size of the attack, which presents clear plateau regions and regions of transition between them. This correlates with strong oscillations in the final size of the system as a function of the size of the attack. We also study these different regions through comparing the distributions of betweenness at different stages of the cascade for different realizations.