给定度序列的有向图的构造与抽样
Constructing and sampling directed graphs with given degree sequences
摘要：
复杂网络的组成部分之间的相互作用往往是有方向的。正确的建模这样的系统经常需要建设的合奏有向图与一个给定的序列，在和出度。由于具有给定度序列的简单标号图的数量通常非常大，即使对于短序列，也需要抽样方法进行统计研究。目前，有两类主要的生成样本的方法。现有的方法之一，首先产生一个限制类的图，然后使用马尔可夫链蒙特卡罗算法的基础上边交换，以产生其他的实现。由于该过程的混合时间仍然未知，因此不能很好地控制样品的独立性。另一类方法是基于配置模型，由于自环和多个边缘，可能导致不可接受的许多样本拒绝。在这里，我们提出了一个算法，可以直接构造一个给定的二度序列的所有可能的实现由简单的有向图。我们的方法是拒绝自由，保证独立的构造样本，并提供他们的权重。然后，权重可以用于计算网络可观测量的统计平均值，就好像它们是从均匀分布的采样或任何其他选择的分布中获得的一样。
英文摘要：
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of simple labeled graphs with a given degree sequence is typically very large even for short sequences, sampling methods are needed for statistical studies. Currently, there are two main classes of methods that generate samples. One of the existing methods first generates a restricted class of graphs, then uses a Markov Chain Monte-Carlo algorithm based on edge swaps to generate other realizations. As the mixing time of this process is still unknown, the independence of the samples is not well controlled. The other class of methods is based on the Configuration Model that may lead to unacceptably many sample rejections due to self-loops and multiple edges. Here we present an algorithm that can directly construct all possible realizations of a given bi-degree sequence by simple digraphs. Our method is rejection free, guarantees the independence of the constructed samples, and provides their weight. The weights can then be used to compute statistical averages of network observables as if they were obtained from uniformly distributed sampling, or from any other chosen distribution.
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。
