从节点的空间嵌入中分离复杂系统结构的空间网络代理
Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes
摘要：
具有嵌入在度量空间中的节点的网络近年来获得了越来越多的关注。然而，在研究网络的宏观性质时，很少考虑空间嵌入对网络结构特征的影响。在这里，我们提出了一个空模型的层次结构，从一个给定的空间嵌入式网络，可以保持与节点的嵌入在度量空间中的全局和局部统计数据生成随机代理。比较原始网络和所得到的代理的全局特性允许量化这些特性在多大程度上已经由节点和链路的空间嵌入预先确定。我们将我们的框架应用于各种现实世界的空间网络，并表明所提出的模型比不考虑节点空间嵌入的标准随机网络模型更好地捕捉了所研究网络的宏观特性。根据所提出的零模型的实际性能，网络被分为不同的类。由于许多现实世界的复杂网络实际上是空间网络，所提出的方法是相关的解开底层复杂系统结构从空间嵌入的节点在许多领域，从社会系统的基础设施和神经生理学气候。
英文摘要：
Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.
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