This book is devoted to the probabilistic description of the behavior of
a network in the process of random removal of its components (links,
nodes) appearing as a result of technical failures, natural disasters or
intentional attacks. It is focused on a practical approach to network
reliability and resilience evaluation, based on applications of Monte
Carlo methodology to numerical approximation of network combinatorial
invariants, including so-called multidimensional destruction spectra.
This allows to develop a probabilistic follow-up analysis of the network
in the process of its gradual destruction, to identify most important
network components and to develop efficient heuristic algorithms for
network optimal design. Our methodology works with satisfactory accuracy
and efficiency for most applications of reliability theory to real -life
problems in networks.