Related papers: Numerical assessment of the percolation threshold …
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
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…
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of…
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…
In the presented article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the…
In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
We consider loop ensembles on random trees. The loops are induced by a Poisson process of links sampled on the underlying tree interpreted as a metric graph. We allow two types of links, crosses and double bars. The crosses-only case…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
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…
In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
Networks are widely used to model the contact structure within a population and in the resulting models of disease spread. While networks provide a high degree of realism, the analysis of the exact model is out of reach and even numerical…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…
It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
The divergence of the correlation length $\xi$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been…
A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…