Related papers: General theory for extended-range percolation on s…

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…

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…

The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…

We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…

Many real-world networks are embedded in space, and their resilience in the presence of reinforced nodes has not been studied. Here we model such networks using a spatial network model that have an exponential distribution of link length…

Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We…

We consider percolation on interdependent locally treelike networks, recently introduced by Buldyrev et al., Nature 464, 1025 (2010), and demonstrate that the problem can be simplified conceptually by deleting all references to cascades of…

Message passing techniques on networks encompasses a family of related methods that can be employed to ascertain many important properties of a network. It is widely considered to be the state of the art formulation for networked systems…

The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…

In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes…

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…

Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…

Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these…

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair…

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…

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…

Determining design principles that boost robustness of interdependent networks is a fundamental question of engineering, economics, and biology. It is known that maximizing the degree correlation between replicas of the same node leads to…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…