Related papers: Micro-transition cascades to percolation
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…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
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…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability $T_1$ that a node adopting a fad…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier…
Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…