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Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to…
Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance…
In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…
Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of…
Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system…
The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks---communication systems require electricity, while the normal functioning of the power grid relies on communication…
Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
This article determines and characterizes the minimal number of actuators needed to ensure structural controllability of a linear system under structural alterations that can severe the connection between any two states. We assume that…
Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and…
Networks represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity. In many cases, relationships between entities are unambiguously…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex…
Increased coupling between critical infrastructure networks, such as power and communication systems, will have important implications for the reliability and security of these systems. To understand the effects of power-communication…
Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…