We describe a new method for the random sampling of connected graphs with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. Our method builds on a recently introduced novel sampling approach that constructs graphs independently (unlike edge-switching Markov Chain Monte Carlo methods) and efficiently (unlike the configuration model), and extends it to incorporate the constraint of connectivity. Additionally, we present a simple and elegant algorithm for directly constructing a single connected realization of a degree sequence, either as a simple graph or a multigraph. Finally, we demonstrate our sampling method on a realistic scale-free example, as well as on degree sequences of connected real-world networks.

中文翻译：

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连通性很重要：连通图的构建和精确随机抽样

我们描述了一种对具有指定度数序列的连通图进行随机采样的新方法。我们考虑简单图的情况和无环多重图的情况。我们的方法建立在最近引入的一种新颖的采样方法之上，该方法独立地（与边缘切换马尔可夫链蒙特卡罗方法不同）和高效地（与配置模型不同）构建图，并将其扩展为包含连接性约束。此外，我们提出了一种简单而优雅的算法，用于直接构造度数序列的单个连接实现，作为简单图或多重图。最后，我们在一个真实的无标度示例以及连接的现实世界网络的度数序列上演示了我们的采样方法。