Related papers: Epidemic thresholds on scale-free graphs: the inte…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by…
The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the…
We study the non-equilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species $A$ and $B$, and the coupling between them is taken to be asymmetric; $A$ induces $B$ while…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet.…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease…
Disease and information spread over social and information networks. Understanding the spread phenomena in networks requires paying attention not only to the degree distribution but also to the degree correlation. However, it is considered…
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…
For a given, arbitrary graph, what is the epidemic threshold? That is, under what conditions will a virus result in an epidemic? We provide the super-model theorem, which generalizes older results in two important, orthogonal dimensions.…
We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the…
We present a finite-size scaling theory of a contact process with permanent immunity on uncorrelated scale-free networks. We model an epidemic outbreak by an analog of the susceptible-infected-removed model where an infected individual…
Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…