Related papers: Limited path percolation in complex networks
The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…
We consider long-range percolation in dimension $d\geq 1$, where distinct sites $x$ and $y$ are connected with probability $p_{x,y}\in[0,1]$. Assuming that $p_{x,y}$ is translation invariant and that $p_{x,y}=\|x-y\|^{-s+o(1)}$ with $s>2d$,…
We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the…
The shortest-path percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
We study entanglement percolation in qubit-based planar quantum network models of arbitrary topology, where neighboring nodes are initially connected by pure states with quenched disorder in their entanglement. To address this, we develop a…
Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical…
Many topological and dynamical properties of complex networks are defined by assuming that most of the transport on the network flows along the shortest paths. However, there are different scenarios in which non-shortest paths are used to…
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…
In this work, we study the critical long-range percolation on $\mathbb{Z}$, where an edge connects $i$ and $j$ independently with probability $1-\exp\{-\beta |i-j|^{-2}\}$ for some fixed $\beta>0$. Viewing this as a random electric network…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
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…
Entanglement percolation aims at generating maximal entanglement between any two nodes of a quantum network by utilizing strategies based solely on local operations and classical communication between the nodes. As it happens in classical…