15 Robustness and Resilience

Intuitively, a complex network is robust if it keeps its basic functionality even under failure of some of its components. The study of robustness in networks is important because a thorough understanding of the behavior of certain classes of networks under failures and attacks may help to protect, for instance, communication networks like the Internet against assaults or to exploit weaknesses of metabolic networks in drug design. Often, we distinguish between random failure and intentional attacks. Examples for random and intentional component failures in real-world complex networks are, for instance, mutations in a cell, pharmaceutical or environmental stress on metabolic networks, router failures in the Internet, or intentional attacks on airline or highway networks. We will see that some networks like the Internet are very robust against random drop-outs of routers but may suffer heavily from targeted attacks against well-chosen central routers. This chapter is dedicated to network statistics that are of interest with respect to a network’s robustness or its resilience against repeated component failure. We give an overview of a variety of statistics and discuss their applicability in practice in terms of usefulness and computational complexity. Often, research on robustness focuses on how these statistics change, by analyzing or measuring the effects if a network undergoes a sequence of component failures. Wherever possible we try to relate the different statistics and discuss their advantages and disadvantages. In many cases, we use examples to illustrate the definitions. We chose to organize this chapter as follows: We distinguish between worst case, average, and probabilistic statistics. Sections 15.1 and 15.2 cover worst case connectivity and distance measures. Average robustness statistics (Section 15.3) allow a more global perspective on robustness properties whereas probabilistic statistics (Section 15.4) consider the failure probabilities implicitly. While, roughly speaking, the statistics become more and more meaningful the more they are located towards the end of this chapter, they are also more difficult to compute. We conclude this chapter in Section 15.5 with final remarks and list some open problems.