Identification of "Die Hard" nodes in complex networks: A resilience approach

The topology of a network defines the structure on which physical processes dynamically evolve. Even though the topological analysis of these networks has revealed important properties about their organization, the components of real complex networks can exhibit other significant characteristics. In this work we focus in particular on the distribution of the weights associated to the links. Here, a novel metric is proposed to quantify the importance of both nodes and links in weighted scale-free networks in relation to their resilience. The resilience index takes into account the complete connectivity patterns of each node with all the other nodes in the network and is not correlated with other centrality metrics in heterogeneous weight distributions.