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
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