When multiple nodes in a network are subject to failure or loss, the question arises as to whether communication across the resulting degraded network is feasible. Percolation theory and random graph theory have been previously used to answer this question. Here we extend random geometric graph theory to the case of networks with some randomness in bond or edge formation, and we derive a lower bound for bond formation probability. In addition, practical methods to address the little studied question as to how to recover from failures that destroy network connectivity are proposed here.
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