Related papers: Degree-Ordered-Percolation on uncorrelated network…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that…
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by…
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…
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume 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…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
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…
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.…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework…
\emph{Full-bond percolation} with parameter $p$ is the process in which, given a graph, for every edge independently, we delete the edge with probability $1-p$. Bond percolation is motivated by problems in mathematical physics and it is…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
Networks are ubiquitous in diverse real-world systems. Many empirical networks grow as the number of nodes increases with time. Percolation transitions in growing random networks can be of infinite order. However, when the growth of large…
By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic…