Related papers: Percolation on sparse networks
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…
For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…
Because of the non-uniformity of the electric power CPS network and the dynamic nature of the risk propagation process, it is difficult to quantify the critical point of a cyber risk explosion. From the perspective of the dependency…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
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…
We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
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 apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…
We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental statistics and the drive to compete with the…
Spreading models capture key dynamics on networks, such as cascading failures in economic systems, (mis)information diffusion, and pathogen transmission. Here, we focus on design intervention problems -- for example, designing optimal…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…