Related papers: Percolation in real interdependent networks
We explore the robustness of complex networks against physical damage. We focus on spatially embedded network models and datasets where links are physical objects or physically transfer some quantity, which can be disrupted at any point…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
Many real-world networks depend on other networks, often in non-trivial ways, to maintain their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction $1-p$ of nodes in one network randomly…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree…
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…
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant…
Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we…
Highly nonconvex granular particles, such as staples and metal shavings, can form solid-like cohesive structures through geometric entanglement (interlocking). The network structure formed by this entanglement, however, remains largely…
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…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. We consider the the path-loss plus fading model of wireless signal…
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…
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied 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…
Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least $r$ active neighbors. Such process, originally studied on regular structures, has been recently investigated also in…