Forward reachable sets: Analytically derived properties of connected components for dynamic networks.
Forward reachable sets: Analytically derived properties of connected components for dynamic networks.
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DOI：
10.1017/nws.2017.10
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发表时间：
2017-09
期刊：
影响因子：
1.7
通讯作者：
Morris, Martina
中科院分区：
文献类型：
--
作者：
Armbruster, Benjamin;Wang, L I;Morris, Martina
动态网络涌现结构特性的形式化分析在很大程度上是一个未知领域。在这里，我们专注于前向可达集（FRS）作为底层度分布和边缘持续时间的函数的属性。FRS被定义为可以从初始种子经由时间有序边的路径到达的节点的集合;连接分量测度到动态网络的自然扩展。工作在一个随机的框架，我们推导出封闭形式的表达的平均值和方差的指数增长率的FRS的时间网络的边缘和节点的动态。对于具有节点动态的网络，我们计算了FRS增长的阈值。有限的人口规模的影响，探讨通过模拟和近似。我们研究这些属性如何随边缘持续时间和不同的横截面度分布而变化，这些分布表征了一系列科学上有趣的规范性结果（泊松和伯努利）。前向可达集的大小给出了疾病传播网络模型中流行病大小的上限，将这项工作与流行病建模联系起来（Eames，2004）。
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 (; Eames, 2004).