A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network, rather than a sample. Here we propose two methods for obtaining bootstrap samples for networks drawn from latent space models. The first method generates bootstrap replicates of network statistics that can be represented as U-statistics in the latent positions, and avoids actually constructing new bootstrapped networks. The second method generates bootstrap replicates of whole networks, and thus can be used for bootstrapping any network function. Commonly studied network quantities that can be represented as U-statistics include many popular summaries, such as average degree and subgraph counts, but other equally popular summaries, such as the clustering coefficient, are not expressible as U-statistics and thus require the second bootstrap method. Under the assumption of a random dot product graph, a type of latent space network model, we show consistency of the proposed bootstrap methods. We give motivating examples throughout and demonstrate the effectiveness of our methods on synthetic data.

翻译：统计网络分析的一个核心问题是开发古典技术的网络类比。靴式网络数据问题特别具有挑战性,因为通常只观察单一的网络,而不是抽样。这里我们提出从潜伏空间模型中提取的网络获得靴子样本的两种方法。第一种方法产生网络统计数据的靴子样板,在潜伏位置中可以作为U-统计家,并避免实际建造新的靴子网络。第二种方法产生整个网络的靴子样板,因此可以用于任何网络功能的靴子样板。通常研究的网络数量可以作为U-统计家使用,包括许多受欢迎的摘要,例如平均程度和子绘图计数,但其他同样受欢迎的摘要,例如集群系数,并不象U-统计家那样明确,因此需要第二种靴子方法。根据随机点产品图的假设,这是一种潜伏空间网络模型,我们展示了拟议的靴子方法的一致性。我们从整体上进行推介,并展示我们的方法在合成数据上的有效性。