Robustness of complex networks
Robustness, the ability to withstand failures and , is a critical attribute of many complex systems including complex networks.
The study of robustness in complex networks is important for many fields. In ecology, robustness is an important attribute of ecosystems, and can give insight into the reaction to disturbances such as the extinction of species. For biologists, network robustness can help the study of diseases and mutations, and how to recover from some mutations. In economics, network robustness principles can help our understanding of the stability and risks of banking systems. And in engineering, network robustness can help to evaluate the resilience of infrastructure networks such as the Internet or power grids.
The focus of robustness in complex networks is the response of the network to the removal of nodes or links. The mathematical model of such a process can be thought of as an inverse percolation process. Percolation theory models the process of randomly placing pebbles on an n-dimensional lattice with probability p, and predicts the sudden formation of a single large cluster at a critical probability . In percolation theory this cluster is named the percolating cluster. This phenomenon is quantified in percolation theory by a number of quantities, for example the average cluster size . This quantity represents the average size of all finite clusters and is given by the following equation.
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