Network reliability

Network reliability measures the likelihood of overall network functionality (generally various kinds of connectivity) given the probabilities of individual edges functioning. This chapter considers the ramifications of the connection between Tutte polynomials and network reliability. General model of reliability of graphs and a compact representation in terms of reliability polynomials. Network operations for connectedness of target vertex sets; all-terminal reliability is an evaluation of the Tutte polynomial. Bounding the value of the reliability polynomial by computing and bounding its coefficients, primarily using the combinatorial structure of the operating or failed subgraphs. Inequalities for the coefficients in various forms of the all-terminal reliability polynomial. Analytic properties of reliability polynomials (location of roots, shape, and points of inflection). The structure of most reliable graphs and average all-terminal reliability. Extensions to directed graphs.