Related papers: Phase transitions in optimally robust network stru…
Quantum networks are a new paradigm of complex networks, allowing us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that…
From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers.…
It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
We study the tolerance of random networks to intentional attack, whereby a fraction p of the most connected sites is removed. We focus on scale-free networks, having connectivity distribution of P(k)~k^(-a) (where k is the site…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes $N$ and a given cost--which we take as the average number of connections per node $\kav$. We find that the…
Social networks transmitting covert or sensitive information cannot use all ties for this purpose. Rather, they can only use a subset of ties that are strong enough to be ``trusted''. In this paper we consider transitivity as evidence of…
In this paper, we present algorithms for designing networks that are robust to node failures with minimal or limited number of links. We present algorithms for both the static network setting and the dynamic network setting; setting where…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the…
A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such…
The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…
We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale…
This paper deals with the detection and prediction of losses due to cyber attacks waged on vital networks. The accumulation of losses to a network during a series of attacks is modeled by a 2-dimensional monotone random walk process as…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…