Next Article in Journal
Economically Efficient Power Storage Operation by Dealing with the Non-Normality of Power Prediction
Next Article in Special Issue
Adaptive Neuro-Fuzzy Inference Systems as a Strategy for Predicting and Controling the Energy Produced from Renewable Sources
Previous Article in Journal
Effect of Loads and Other Key Factors on Oil-Transformer Ageing: Sustainability Benefits and Challenges
Previous Article in Special Issue
A Critical Review of Robustness in Power Grids Using Complex Networks Concepts
Article Menu

Export Article

Open AccessReview
Energies 2015, 8(10), 12187-12210;

Recent Progress on the Resilience of Complex Networks

Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA
Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100191, China
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
Author to whom correspondence should be addressed.
Academic Editor: Hermann de Meer
Received: 2 July 2015 / Revised: 18 September 2015 / Accepted: 9 October 2015 / Published: 27 October 2015
(This article belongs to the Special Issue Resilience of Energy Systems)
Full-Text   |   PDF [6837 KB, uploaded 27 October 2015]   |  


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 Energies 2015, 8 12188 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. View Full-Text
Keywords: network of networks (NON); percolation; spatially-embedded networks; dynamic networks; spontaneous recovery network of networks (NON); percolation; spatially-embedded networks; dynamic networks; spontaneous recovery

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Gao, J.; Liu, X.; Li, D.; Havlin, S. Recent Progress on the Resilience of Complex Networks. Energies 2015, 8, 12187-12210.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Energies EISSN 1996-1073 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top