Related papers: Percolation on sparse networks
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…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
In this paper we offer a solution to a long-standing problem in the study of networks. Message passing is a fundamental technique for calculations on networks and graphs. The first versions of the method appeared in the 1930s and over the…
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…
Hypergraph networks are closer to real life because they can reflect higher-order interactions, so researchers have begun using them to build models for real-world networks. The mean-field approach is the current tool for studying the…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
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…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
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…
Message passing techniques on networks encompasses a family of related methods that can be employed to ascertain many important properties of a network. It is widely considered to be the state of the art formulation for networked systems…
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…
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…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
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…