Random graphs and networks: limits, approximations, and applications

我们将考虑随机图的一些模型，其中一些节点可能比其他节点形成更多的连接。这些模型包括非齐次图和配置模型。我们的目标是研究这些图的连通性的各种措施，例如随机选择的节点形成集团或其他子图的概率。我们的目标是找到渐近以及这些措施的连通性的近似图的大小是无穷大。这里可以应用的技术包括Stein的概率近似法。这项工作的扩展包括类似的结果动态随机图演变的时间和随机过程的随机图。

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.