Recent Progress on the Resilience of Complex Networks

Energies

Jianxi Gao¹  Xueming Liu³  Daqing Li⁴  Shlomo Havlin² 

[1] Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA; E-Mail:;Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel; E-Mail:;Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; E-Mail:;School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China

关键词: network of networks (NON);    percolation;    spatially-embedded networks;    dynamic networks;    spontaneous recovery;   

DOI  :  10.3390/en81012187

来源: mdpi

【 摘 要 】

Many complex systems in the real world can be modeled as complex networks, which has captured in recent years enormous attention from researchers of diverse fields ranging from natural sciences to engineering. The extinction of species in ecosystems and the blackouts of power girds in engineering exhibit the vulnerability of complex networks, investigated by empirical data and analyzed by theoretical models. For studying the resilience of complex networks, three main factors should be focused on: the network structure, the network dynamics and the failure mechanism. In this review, we will introduce recent progress on the resilience of complex networks based on these three aspects. For the network structure, increasing evidence shows that biological and ecological networks are coupled with each other and that diverse critical infrastructures interact with each other, triggering a new research hotspot of “networks of networks” (NON), where a network is formed by interdependent or interconnected networks. The resilience of complex networks is deeply influenced by its interdependence with other networks, which can be analyzed and predicted by percolation theory. This review paper shows that the analytic framework for NON yields novel percolation laws for n interdependent networks and also shows that the percolation theory of a single network studied extensively in physics and mathematics in the last 60 years is a specific limited case of the more general case of n interacting networks. Due to spatial constraints inherent in critical infrastructures, including the power gird, we also review the progress on the study of spatially-embedded interdependent networks, exhibiting extreme vulnerabilities compared to their non-embedded counterparts, especially in the case of localized attack. For the network dynamics, we illustrate the percolation framework and methods using an example of a real transportation system, where the analysis based on network dynamics is significantly different from the structural static analysis. For the failure mechanism, we here review recent progress on the spontaneous recovery after network collapse. These findings can help us to understand, realize and hopefully mitigate the increasing risk in the resilience of complex networks.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.