Applying Percolation Theory

Unlike the previous chapter where propagation of failures along the dependency links was studied in a qualitative, human-judgment fashion, this chapter offers an approach to analyzing resilience to failure propagation via a rigorous use of percolation theory. In percolation theory, the basic idea is that a node failure or an edge failure (reverse) percolates throughout a network, and, accordingly, the failure affects the connectivity among nodes. The degree of network resilience can be measured by the size of a largest component (or cluster) after a fraction of nodes or edges are removed in the network. In many cybersecurity applications, the underlying ideas of percolation theory have not been much explored. In this chapter, it is explained how percolation theory can be used to measure network resilience in the process of dealing with different types of network failures. It introduces the measurement of adaptability and recoverability in addition to that of fault tolerance as new contributions to measuring network resilience by applying percolation theory.

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