Random graphs and networks: limits, approximations, and applications

我们将考虑一些随机图的模型，其中一些节点可能形成比其他节点更多的连接。这些模型包括非齐次图和配置模型。我们的目标是研究这类图的连通性的各种度量，例如随机选择的节点形成团或其他子图的概率。我们的目标是找到这些连通性度量的渐近性和近似值，因为图的大小将达到无穷大。这里可以应用的技术包括斯坦的概率近似方法。这一工作的推广包括动态随机图随时间演化的类似结果和随机图上随机过程的类似结果。

We will consider some models for random graphs where some nodes may form more connections than others. Such models include non-homogeneous graphs and configuration models. We aim to study various measures of connectedness of such graphs, for instance the probabilities of randomly chosen nodes forming cliques or other subgraphs. We aim to find asymptotics as well as approximations for these measures of connectedness as the size of the graph is going to infinity. Techniques which could be applied here include Stein's method for probability approximations. Extensions of this work include analogous results for dynamic random graphs evolving in time and for stochastic processes on random graphs.