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Many complex systems may be described not by one, but by a number of complex networks mapped one on the other in a multilayer structure. The interactions and dependencies between these layers cause that what is true for a distinct single…

Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n…

Real-world complex systems exhibit intricate interconnections and dependencies, especially social networks, technological infrastructures, and communication networks. These networks are prone to disconnection due to random failures or…

Network's resilience to the malfunction of its components has been of great concern. The goal of this work is to determine the network design guidelines, which maximizes the network efficiency while keeping the cost of the network (that is…

It is a mainstream idea that scale-free network would be fragile under the selective attacks. Internet is a typical scale-free network in the real world, but it never collapses under the selective attacks of computer viruses and hackers.…

Maximizing robustness and minimizing cost are common objectives in the design of infrastructure networks. However, most infrastructure networks evolve and operate in a highly decentralized fashion, which may significantly impact the…

Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially…

To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given…

Much of our commerce and traveling depend on the efficient operation of large scale networks. Some of those, such as electric power grids, transportation systems, communication networks, and others, must maintain their efficiency even after…

Single- and multi-layer complex networks have been proven as a powerful tool to study the dynamics within social, technological,or natural systems. An often observed common goal there is to optimize these systems for specific purposes by…

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered…

Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…

In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of…

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we…

In today's networked society, many real-world problems can be formalized as predicting links in networks, such as Facebook friendship suggestions, e-commerce recommendations, and the prediction of scientific collaborations in citation…

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…

Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links' weight, triggers a…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…

The behavior of complex networks under attack depends strongly on the specific attack scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure or attack but appear to be especially…