生成具有指定度分布的简单随机图
Generating simple random graphs with prescribed degree distribution
摘要：
设$F$是支持非负整数的概率分布。描述并比较了四种生成具有（近似）度分布$F$的简单无向图的方法。两种方法是基于所谓的配置模型与修改，确保一个单图，一种方法是经典的Erdens-Rényi图的扩展，其中的边缘概率是随机变量，最后一种方法开始于一个有向随机图，然后修改为一个简单的无向图。所有的方法都给出了正确的分布在大图的大小的限制，但在不同的假设下的度分布$F$，也使用不同的操作顺序。
英文摘要：
Let $F$ be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution $F$ are described and compared. Two methods are based on the so called configuration model with modifications ensuring a simple graph, one method is an extension of the classical Erdős-Rényi graph where the edge probabilities are random variables, and the last method starts with a directed random graph which is then modified to a simple undirected graph. All methods are shown to give the correct distribution in the limit of large graph size, but under different assumptions on the degree distribution $F$ and also using different order of operations.
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。
