Preferential attachment networks: Robustness and Vulnerability

Preferential attachment networks are a class of dynamical networks in which new nodes are connected to existing nodes with a probability proportional to an increasing function of their degree. Asymptotically the degree distributions of these networks follow a power law with tunable power law exponent tau. In this talk I survey recent results, obtained in collaboration with Steffen Dereich and Maren Eckhoff, on robustness and vulnerability of these networks. In particular we show that in the regime 2<tau<3 the qualitative behaviour of the network remains unchanged by random deletion of an arbitrarily large proportion of the edges, while it changes radically if an arbitrarily small proportion of carefully selected vertices is removed.