Related papers: Exhaustive percolation on random networks
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
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…
Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a…
We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependent relations are randomly built between nodes of networks A and B. In our model we assume that each…
We present derivations of the contagion condition for a range of spreading mechanisms on families of generalized random networks and bipartite random networks. We show how the contagion condition can be broken into three elements, two…
In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion…
\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…
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula…
This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study…
We study a rumour model from a percolation theory and branching process point of view. The existence of a giant component is related to the event where the rumour spreads out trough an infinite number of individuals. We present sharp lower…
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially…
Large-scale power blackouts caused by cascading failure are inflicting enormous socioeconomic costs. We study the problem of cascading link failures in power networks modelled by random geometric graphs from a percolation-based viewpoint.…
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…
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…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…