Abstract
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.
Highlights
Networks have become a ubiquitous tool in understanding both natural and engineered systems, including, climate systems [1], physiological systems [2], civil infrastructure systems [3, 4], social interactions [5,6,7,8], and biochemical reactions [9]
Our results indicate that diverging tail, hub-andspoke, tree, and crossing path topologies require the recoverability of all links to return to their original performance as their directed topology includes no cycle
We argue that our analysis embodies the transition of natural and engineered systems from the disrupted state to the recovered state, and quantifies the effect of network topology on facilitating or impeding this transition
Summary
Networks have become a ubiquitous tool in understanding both natural and engineered systems, including, climate systems [1], physiological systems [2], civil infrastructure systems [3, 4], social interactions [5,6,7,8], and biochemical reactions [9]. As the overarching goal of the current study, is to equip scientists and practitioners with the knowledge and tools necessary to characterize the nexus of network topology and recoverability This is achieved through an integrated study of networks with different topological patterns and sizes in the face of attacks, which drastically compromise the performance of networks by demolishing a set of links or the total network. Our empirical findings demonstrate how and to what extent adding redundant paths elevates the robustness of the network This adds to the knowledge of identifying the performance of residual network topologies following the recovery of each component. The recoverability measure indicates the proportion of links that can remain disrupted while the network delivers the total initial demand This happens when the network is fully disrupted and requires the restoration of all links to reach φGjLj. Third, the maximum value of RGðN; LÞ equals one, obtained when |S| = 0. This happens when the network requires the restoration of no links to reach φGjLj
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