We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are two of the most commonly needed ones when constructing null models for the practical analysis of physical or biological networks. Yet handling these constraints, letalone combining them, is non-trivial. Our method builds on a recently introduced novel sampling approach that constructs graphs with given degrees independently (unlike edge-switching Markov chain Monte Carlo methods) and efficiently (unlike the configuration model), and extends it to incorporate the constraint of connectedness. 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, and show that enforcing connectedness can significantly alter the properties of sampled networks.

我们描述了一种用于以指定的度数序列对连接的网络进行随机采样的新方法。我们同时考虑简单图和无环多图的情况。当构建用于物理或生物网络的实际分析的空模型时，固定程度和连接性的约束是最常用的两个约束。然而，处理这些约束，更不用说将它们组合起来是不平凡的。我们的方法基于最近引入的新颖采样方法，该方法可以独立（与边缘切换马尔可夫链蒙特卡洛方法不同）且有效地（与配置模型不同）构造具有给定度数的图，并将其扩展以合并连接的约束。此外，我们提出了一种简单而优雅的算法，可以直接构造一个简单的图形或多图形的度数序列的连接实现。最后，我们在一个现实的无标度示例以及连接的实际网络的度序列上演示了我们的采样方法，并表明强制连接可以显着改变采样网络的属性。