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Mathematical theories and empirical evidence suggest that several complex natural and man-made systems are fragile: as their size increases, arbitrarily small and localized alterations of the system parameters may trigger system-wide failures. Examples are abundant, from perturbation of the population densities leading to extinction of species in ecological networks [1], to structural changes in metabolic networks preventing reactions [2], cascading failures in power networks [3], and the onset of epileptic seizures following alterations of structural connectivity among populations of neurons [4]. While fragility of these systems has long been recognized [5], convincing theories of why natural evolution or technological advance has failed, or avoided, to enhance robustness in complex systems are still lacking. In this paper we propose a mechanistic explanation of this phenomenon. We show that a fundamental tradeoff exists between fragility of a complex network and its controllability degree, that is, the control energy needed to drive the network state to a desirable state. We provide analytical and numerical evidence that easily controllable networks are fragile, suggesting that natural and man-made systems can either be resilient to parameters perturbation or efficient to adapt their state in response to external excitations and controls.
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A Spectral Measure for Network Robustness: Assessment, Design, and Evolution
A robust system should perform well under random failures or targeted attacks, and networks have been widely used to model the underlying structure of complex systems such as communication, infrastructure, and transportation networks. Hence, network robustness becomes critical to understanding system robustness. In this paper, we propose a spectral measure for network robustness: the second spectral moment m2 of the network. Our results show that a smaller second spectral moment m2 indicates a more robust network. We demonstrate both theoretically and with extensive empirical studies that the second spectral moment can help (1) capture various traditional measures of network robustness; (2) assess the robustness of networks; (3) design networks with controlled robustness; and (4) study how complex networked systems (e.g., power systems) behave under cascading failures.
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- Award ID(s):
- 2144918
- PAR ID:
- 10398082
- Date Published:
- Journal Name:
- 2022 IEEE International Conference on Knowledge Graph (ICKG)
- Page Range / eLocation ID:
- 97 to 104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICKG55886.2022.00020
