Related papers: Spectral Anlysis on Explosive Percolation
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
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…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
Comparing with single networks, the multiplex networks bring two main effects on the spreading process among individuals. First, the pathogen or information can be transmitted to more individuals through different layers at one time, which…
Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
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…
In this paper, we study the dynamics of a viral spreading process in random geometric graphs (RGG). The spreading of the viral process we consider in this paper is closely related with the eigenvalues of the adjacency matrix of the graph.…
The spectral evolution model aims to characterize the growth of large networks (i.e., how they evolve as new edges are established) in terms of the eigenvalue decomposition of the adjacency matrices. It assumes that, while eigenvectors…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
The diffusion model is used to calculate the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered…
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…
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…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant…
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…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
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…
With the emerging of new networks, such as wireless sensor networks, vehicle networks, P2P networks, cloud computing, mobile Internet, or social networks, the network dynamics and complexity expands from system design, hardware, software,…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…