Measuring cascade effects in interdependent networks by using effective graph resistance

Understanding the correlation between the underlie network structure and overlay cascade effects in the interdependent networks is one of major challenges in complex network studies. There are some existing metrics that can be used to measure the cascades. However, different metrics such as average node degree interpret different characteristic of network topological structure, especially less metrics have been identified to effectively measure the cascading performance in interdependent networks. In this paper, we propose to use a combined Laplacian matrix to model the interdependent networks and their interconnectivity, and then use its effective resistance metric as an indicator to its cascading behavior. Moreover, we have conducted extensive comparative studies among different metrics such as average node degree, and the proposed effective resistance. We have found that the effective resistance metric can describe more accurate and finer characteristics on topological structure of the interdependent networks than average node degree which is widely adapted by the existing research studies for measuring the cascading performance in interdependent networks

Using interdependency matrices to mitigate targeted attacks on interdependent networks: A case study involving a power grid and backbone telecommunications networks

Analysis of the interdependencies between interconnected critical infrastructures can help enhance the robustness of the individual infrastructures as well as the overall interconnected infrastructures. One of the most studied interdependent critical infrastructure network scenarios is a power grid connected to a backbone telecommunications network. In this interdependent infrastructure scenario, the robustness of the entire system is usually analyzed in the context of cascading failure models in the power grid. However, this paper focuses on targeted attacks, where an attack on a telecommunications network node directly affects a connected power grid node, and vice versa. Cascading failures are outside the scope of this paper because the objective is to enhance the robustness of the interconnections between the infrastructures. In order to mitigate the impacts of targeted attacks on the interdependent infrastructures, three interdependency matrices for connecting the infrastructures are specified and analyzed. The analysis identifies the interdependency matrix that best reduces the impacts of targeted attacks and the propagation of failures between the infrastructures. Additionally, the impacts of interconnecting a power grid to different telecommunications networks, each with different susceptibilities to targeted attacks, is evaluate

A Critical Review of Robustness in Power Grids using Complex Networks Concepts

Complex network theory for analyzing robustness in energy gridsThis paper reviews the most relevant works that have investigated robustness in power grids using Complex Networks (CN) concepts. In this broad field there are two different approaches. The first one is based solely on topological concepts, and uses metrics such as mean path length, clustering coefficient, efficiency and betweenness centrality, among many others. The second, hybrid approach consists of introducing (into the CN framework) some concepts from Electrical Engineering (EE) in the effort of enhancing the topological approach, and uses novel, more efficient electrical metrics such as electrical betweenness, net-ability, and others. There is however a controversy about whether these approaches are able to provide insights into all aspects of real power grids. The CN community argues that the topological approach does not aim to focus on the detailed operation, but to discover the unexpected emergence of collective behavior, while part of the EE community asserts that this leads to an excessive simplification. Beyond this open debate it seems to be no predominant structure (scale-free, small-world) in high-voltage transmission power grids, the vast majority of power grids studied so far. Most of them have in common that they are vulnerable to targeted attacks on the most connected nodes and robust to random failure. In this respect there are only a few works that propose strategies to improve robustness such as intentional islanding, restricted link addition, microgrids and smart grids, for which novel studies suggest that small-world networks seem to be the best topology.This work has been partially supported by the project TIN2014-54583-C2-2-R from the Spanish Ministerial Commission of Science and Technology (MICYT), by the project S2013/ICE-2933 from Comunidad de Madrid and by the project FUTURE GRIDS-2020 from the Basque Government

Complex Networks from Classical to Quantum

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Cascading Failures in Complex Networks

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.Comment: This review has been accepted for publication in the Journal of Complex Networks Published by Oxford University Pres

Network science based quantification of resilience demonstrated on the Indian Railways Network

The structure, interdependence, and fragility of systems ranging from power grids and transportation to ecology, climate, biology and even human communities and the Internet, have been examined through network science. While the response to perturbations has been quantified, recovery strategies for perturbed networks have usually been either discussed conceptually or through anecdotal case studies. Here we develop a network science-based quantitative methods framework for measuring, comparing and interpreting hazard responses and as well as recovery strategies. The framework, motivated by the recently proposed temporal resilience paradigm, is demonstrated with the Indian Railways Network. The methods are demonstrated through the resilience of the network to natural or human-induced hazards and electric grid failure. Simulations inspired by the 2004 Indian Ocean Tsunami and the 2012 North Indian blackout as well as a cyber-physical attack scenario. Multiple metrics are used to generate various recovery strategies, which are simply sequences in which system components should be recovered after a disruption. Quantitative evaluation of recovery strategies suggests that faster and more resource-effective recovery is possible through network centrality measures. Case studies based on two historical events, specifically the 2004 Indian Ocean tsunami and the 2012 North Indian blackout, and a simulated cyber-physical attack scenario, provides means for interpreting the relative performance of various recovery strategies. Quantitative evaluation of recovery strategies suggests that faster and more resource-effective restoration is possible through network centrality measures, even though the specific strategy may be different for sub-networks or for the partial recovery

Optimizing topological cascade resilience based on the structure of terrorist networks

Complex socioeconomic networks such as information, finance and even terrorist networks need resilience to cascades - to prevent the failure of a single node from causing a far-reaching domino effect. We show that terrorist and guerrilla networks are uniquely cascade-resilient while maintaining high efficiency, but they become more vulnerable beyond a certain threshold. We also introduce an optimization method for constructing networks with high passive cascade resilience. The optimal networks are found to be based on cells, where each cell has a star topology. Counterintuitively, we find that there are conditions where networks should not be modified to stop cascades because doing so would come at a disproportionate loss of efficiency. Implementation of these findings can lead to more cascade-resilient networks in many diverse areas.Comment: 26 pages. v2: In review at Public Library of Science ON