Armbruster Benjamin, Wang L I, Morris Martina
Northwestern University, Industrial Engineering and Management Sciences, Evanston, IL, USA.
Statistics, University of Washington, Seattle, WA, USA.
Netw Sci (Camb Univ Press). 2017 Sep;5(3):328-354. doi: 10.1017/nws.2017.10. Epub 2017 Jun 29.
Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).
对动态网络新兴结构特性的形式化分析在很大程度上仍是未知领域。我们在此关注前向可达集（FRS）的特性，它是潜在度分布和边持续时间的函数。FRS被定义为可以通过按时间顺序排列的边的路径从初始种子节点到达的节点集；这是将连通分量度量自然扩展到动态网络。在一个随机框架中，我们推导出了具有边和节点动态的时间网络中FRS指数增长率的均值和方差的闭式表达式。对于具有节点动态的网络，我们计算了FRS增长的阈值。通过模拟和近似探讨了有限种群规模的影响。我们研究了这些特性如何因边持续时间以及表征一系列具有科学意义的规范结果（泊松和伯努利）的不同横截面度分布而变化。前向可达集的大小为疾病传播网络模型中的流行规模提供了一个上限，将这项工作与流行病建模联系起来（弗格森，2000；伊姆斯，2004）。
