Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA.
Sci Rep. 2020 Jul 16;10(1):11775. doi: 10.1038/s41598-020-68583-1.
Spatially-embedded networks represent a large class of real-world networks of great scientific and societal interest. For example, transportation networks (such as railways), communication networks (such as Internet routers), and biological networks (such as fungal foraging networks) are all spatially embedded. Both the density of interactions (presence of edges) and intensity of interactions (edge weights) are typically found to decrease as a function of spatial separation of nodes in these networks. Communication and mobility of groups of individuals have also been shown to decline with their spatial separation, and the so-called gravity model postulates that this decline takes the form of a power-law holding at all distances. There is however some evidence that the rate of decline might change as the distance increases beyond a certain value, called a change point, but there have been few statistically principled methods for determining the existence and location of change points or assessing the change in intensity of interactions associated with them. We introduce such a method within the Bayesian paradigm and apply it to anonymized mobile call detail records (CDRs). Our results are potentially useful in settings where understanding social and spatial mixing of people is important, such as in the design of cluster randomized trials for studying interventions for infectious diseases, but we also anticipate the method to be useful for investigating more generally how distance may affect tie strengths in general in spatially embedded networks.
嵌入空间的网络代表了一大类具有重要科学和社会意义的真实网络。例如，交通网络（如铁路）、通信网络（如互联网路由器）和生物网络（如真菌觅食网络）都是嵌入空间的。在这些网络中，节点之间的空间分离会导致相互作用的密度（边的存在）和强度（边权重）呈下降趋势。已经证明，群体的通信和移动性随着它们的空间分离而下降，所谓的引力模型假定这种下降形式在所有距离上都保持幂律。然而，有一些证据表明，随着距离超过某个值（称为变化点）的增加，下降速度可能会发生变化，但目前还没有用于确定变化点的存在和位置以及评估与之相关的相互作用强度变化的统计原则方法。我们在贝叶斯范例中引入了这样一种方法，并将其应用于匿名移动通话详细记录（CDR）。我们的结果在理解人员的社会和空间混合很重要的环境中可能是有用的，例如在设计用于研究传染病干预措施的集群随机试验中，但我们也预计该方法可用于更广泛地研究距离如何影响一般嵌入空间网络中的联系强度。
