Related papers: Percolation in real multiplex networks
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…
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…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
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 present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study…
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…
We extend the observability model to multiplex networks. We present mathematical frameworks, valid under the treelike ansatz, able to describe the emergence of the macroscopic cluster of mutually observable nodes in both synthetic and…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
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,…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…