一个加权配置模型与非齐次流行病
A weighted configuration model and inhomogeneous epidemics
摘要：
提出了一种具有指定度分布和度相关边权值的随机图模型。每个顶点独立地配备有随机数的半边，并且每个半边根据允许取决于其顶点的度的分布被分配整数值的权重。然后，具有相同权重的半边随机配对以创建边。一个表达式的阈值出现的一个巨大的组件在所得到的图是来自使用多类型的分支过程的结果。同样的技术也给出了一个表达式的基本再生数的流行病在图中的概率，某一边缘被用于传输是一个函数的边缘权重。它表明，如果具有大的程度的顶点往往有大（小）的权重在其边缘上，如果传输概率与边的权重增加，那么它是更容易（更难）的流行病起飞相比，一个随机化的流行病具有相同的程度和权重分布。还给出了计算流行病大爆发概率和爆发规模的方法。最后，该模型适合三个经验加权网络的重要性传染病的传播，它表明，$R_0$可以大大超过或低估，如果不考虑程度和权重之间的相关性。
英文摘要：
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 according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight. It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that $R_0$ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
