Recovery patterns and physics of the network.

In a progressively interconnected world, the loss of system resilience has consequences for human health, the economy, and the environment. Research has exploited the science of networks to explain the resilience of complex systems against random attacks, malicious attacks, and the localized attacks induced by natural disasters or mass attacks. Little is known about the elucidation of system recovery by the network topology. This study adds to the knowledge of network resilience by examining the nexus of recoverability and network topology. We establish a new paradigm for identifying the recovery behavior of networks and introduce the recoverability measure. Results indicate that the recovery response behavior and the recoverability measure are the function of both size and topology of networks. In small sized networks, the return to recovery exhibits homogeneous recovery behavior over topology, while the return shape is dispersed with an increase in the size of network. A network becomes more recoverable as connectivity measures of the network increase, and less recoverable as accessibility measures of network increase. Overall, the results not only offer guidance on designing recoverable networks, but also depict the recovery nature of networks deliberately following a disruption. Our recovery behavior and recoverability measure has been tested on 16 distinct network topologies. The relevant recovery behavior can be generalized based on our definition for any network topology recovering deliberately.