Vulnerability of networks of interacting Markov chains

Abstract

The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node, but also on the statuses of the neighboring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for three real networks: network of infrastructures, power grid, and WWW, identifying the most influential nodes of these networks.