Related papers: A weighted configuration model and inhomogeneous e…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…
The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where…
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…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…
Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…