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We develop a graph-theoretic model for service-oriented networks and propose metrics that quantify the resilience of such networks under node and edge failures. These metrics are based on the topological structure of the network and the manner in which services are distributed over the network. We present efficient algorithms to determine the maximum number of node and edge failures that can be tolerated by a given service-oriented network. These algorithms rely on known algorithms for computing minimum cuts in graphs. We also present efficient algorithms for optimally allocating services over a given network so that the resulting service-oriented network can tolerate single node or edge failures. These algorithms are derived through a careful analysis of the decomposition of the underlying network into appropriate types of connected components.