Spatially embedded random networks
Spatially embedded random networks
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DOI：
10.1103/physreve.76.056115
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发表时间：
2007-11-01
影响因子：
2.4
通讯作者：
Bullock, S.
中科院分区：
文献类型：
--
作者：
Barnett, L.;Di Paolo, E.;Bullock, S.
现代网络理论分析的许多现实世界网络都具有自然的空间元素；例如，互联网、社交网络、神经网络等。然而，除了相对少量的有些专业化和特定领域的研究外，空间元素大多被忽视，特别是它与网络结构的关系。在本文中，我们介绍了一个模型框架来通过空间嵌入来分析网络结构的中介；具体来说，我们将连通性建模为依赖于网络节点之间的距离。我们的空间嵌入随机网络构建主要不是为了作为任何特定类别的现实世界网络的准确模型，而是为了获得空间嵌入对网络结构影响的直觉；然而，我们能够在相当一般的环境中证明空间嵌入对连通性的一些限制，例如空间对称性的影响、无标度度分布的条件以及小世界空间网络的存在。我们还导出了一些空间嵌入网络的标准结构统计数据，并通过具体示例说明了我们的模型框架的应用。
Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples.