The Resilience of a Complex Network

The resilience of a network is identifiable by its ability to absorb external shocks. Such a concept is strongly related to the topology of the graph underlying the network, the definition of shock and how it propagates over the system. Undoubtedly, impulses at the single node or arc level are relevant for the macroscopic fluctuations of the entire network. The analysis of the resilience of a network is of crucial relevance in economics, finance and social science. Indeed, it has natural connections with the assessment of the stability of a system and with systemic risk. This chapter deals with this topic. Specifically, it reviews theoretical proposals for measuring the resilience of a network by taking peculiar care of the cases of weighted and directed networks.