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Network-wide migrations of a running network, such as the replacement of a routing protocol or the modification of its configuration, can improve the performance, scalability, manageability, and security of the entire network. However, such migrations are an important source of concerns for network operators as the reconfiguration campaign can lead to long, service-disrupting outages. In this paper, we propose a methodology that addresses the problem of seamlessly modifying the configuration of link-state Interior Gateway Protocols (IGPs). We illustrate the benefits of our methodology by considering several migration scenarios, including the addition and the removal of routing hierarchy in a running IGP, and the replacement of one IGP with another. We prove that a strict operational ordering can guarantee that the migration will not create any service outage. Although finding a safe ordering is NP-complete, we describe techniques that efficiently find such an ordering and evaluate them using several real-world and inferred ISP topologies. Finally, we describe the implementation of a provisioning system that automatically performs the migration by pushing the configurations on the routers in the appropriate order while monitoring the entire migration process.