Effective measurement of network vulnerability under random and intentional attacks

The study of the security and stability of complex networks plays a central role in reducing the risk and consequences of attacks or disfunctions of any type. The concept of vulnerability helps to measure the response of complex networks subjected to attacks on vertices and edges and it allows to spot the critical component of a network in order to improve its security. We introduce an accurate and computable definition of network vulnerability which is directly connected with its topology and we analyze its basic properties. We discuss the relationship of the vulnerability with other parameters of the network and we illustrate this with some examples.