相关论文: Exact solution of site and bond percolation on sma…

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…

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 study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that…

Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for…

The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…

In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…

In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the…

The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment,…

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…

We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation…

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…

To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the…

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide…

We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by…

The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of…

We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be $p_c ({\rm bond})=0.248\,811\,82(10)$ and $p_c ({\rm site})=0.311\,607\,7(2)$. By…

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…