Related papers: How clustering affects the bond percolation thresh…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
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…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
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…
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…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition…
It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)],…
Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We study the influence of clustering, more specifically triangles, on cascading failures in interdependent networks or systems, in which we model the dependence between comprising systems using a dependence graph. First, we propose a new…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
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…
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…
Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…
The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…