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Phasor Measurement Units (PMU), due to their capability for providing highly precise and time-synchronized measurements of synchrophasors, have now become indispensable in wide area monitoring of power-grid systems. Successful and reliable delivery of synchrophasor packets from the PMUs to the Phasor Data Concentrators (PDCs) and beyond, requires a backbone communication network that is robust and resilient to failures. These networks are vulnerable to a range of failures that include cyber-attacks, system or device level outages and link failures. In this paper, we present a framework to evaluate the resilience of a PMU network in the context of link failures. We model the PMU network as a connected graph and link failures as edges being removed from the graph. Our approach, inspired by model checking methods, involves exhaustively checking the reachability of PMU nodes to PDC nodes, for all possible combinations of link failures, given an expected number of links fail simultaneously. Using the IEEE 14-bus system, we illustrate the construction of the graph model and the solution design. Finally, a comparative evaluation on how adding redundant links to the network improves the Power System Observability, is performed on the IEEE 118 bus-system.