The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree structure alone. A Markov chain Monte Carlo (MCMC) algorithm, based on a degree-preserving double-edge swap, provides an asymptotic solution to sample from the configuration model. However, accurately and efficiently detecting this Markov chain's convergence on its stationary distribution remains an unsolved problem. Here, we provide a solution to detect convergence and sample from the configuration model. We develop an algorithm, based on the assortativity of the sampled graphs, for estimating the gap between effectively independent MCMC states, and a computationally efficient gap-estimation heuristic derived from analyzing a corpus of 509 empirical networks. We provide a convergence detection method based on the Dickey-Fuller Generalized Least Squares test, which we show is more accurate and efficient than three alternative Markov chain convergence tests.

翻译：配置模型是标准工具，用于均匀生成具有指定度序列的随机图，常作为零模型来评估观测网络结构中有多少可仅由其度结构解释。基于保持度分布的双边交换的马尔可夫链蒙特卡罗（MCMC）算法，为从配置模型中采样提供了渐近解。然而，准确高效地检测该马尔可夫链在平稳分布上的收敛性仍是未解难题。本文提出一种检测收敛性并从配置模型采样的解决方案。我们开发了一种基于采样图同配性的算法，用于估计有效独立MCMC状态之间的间隔，并通过分析509个经验网络语料库推导出计算高效的间隔估计启发式方法。我们还提供基于迪基-富勒广义最小二乘检验的收敛检测方法，证明该方法比三种替代的马尔可夫链收敛检验更准确高效。