Attack vulnerability of scale -free network due to cascade breakdown
As we discussed in the class for the information cascade model, a complex networks can be brought down by attack on a single or a very few nodes through the process of cascading failures. Here in the research by Liao Zhao, Kwangho Park and Ying-Cheng Lai, a recent model for cascading failures in complex networks and uncover a phase- transition point as been investigated, where cascading failures can cause the network to disintegrated almost entirely.
The work by Albert demonstrated that scale-free networks possess the robust-yet-fragile property, in the sense that they are robust against random failures of nodes but fragile to intentional attacks, the fragility here means that a scale-free network can become disintegrated under attacks on a small but still appreciable set of nodes that include a substantial fraction of links in the network. Since generally, an attack on a single or very few nodes will not bring down the network. Note that this interesting result only based on purely scale-free networks. In other words, dynamics in the network, how information or load is distributed in the network, for example was not taken into account.
Investigators did a lot of researches and studies in cascading failures triggered by attacks on a single or a few nodes in a scale-free networks in a more quantitative manner and focused on the fundamentally and practically important question of whether such failure can lead to the disintegration of the a network. And they find that a phase-transition -like phenomenon in terms of the network tolerance parameter characterizing the node capacity, where the two distinct phase correspond to the situations where the network under attack remains largely integrated or disintegrated as a result of cascading failures. A theoretical estimation for the phase-transition point and provided numerical check has been obtained. These results might be useful in important areas such as network security.
http://journals.aps.org/pre/pdf/10.1103/PhysRevE.70.035101
http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch19.pdf