Related papers: Critical Percolation on Random Networks with Presc…
Majority bootstrap percolation is a model of infection spreading in networks. Starting with a set of initially infected vertices, new vertices become infected once half of their neighbours are infected. Balogh, Bollob\'{a}s and Morris…
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,…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Random graph models have been instrumental in characterizing complex networks, but chemical reaction networks (CRNs) are better represented as hypergraphs. Traditional models of random CRNs often reduce CRNs to bipartite graphs,…
We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that the failure probability of a node depends on its degree (number of…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…
Detecting and characterizing community structure plays a crucial role in the study of networked systems. However, there is still a lack of understanding of how community structure affects the systems' resilience and stability. Here, we…
Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph…
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied.…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, which are known to depend on topology, can also be explored by tuning the form of the…
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
We show that a simple model for the propagation of a rumor on a small-world network exhibits critical behavior at a finite randomness of the underlying graph. The transition occurs between a regime where the rumor "dies" in a small…