Related papers: Hidden transition in multiplex networks
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…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at 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…
From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers).…
In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
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…
We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the…
Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation…
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…
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…
We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random…
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
Multilayer systems are coupled networks characterized by different contexts (layers) of interaction and have gained much attention recently due to their suitability to describe a broad spectrum of empirical complex systems. They are very…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…