Dimension of spatially embedded networks
Dimension of spatially embedded networks
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DOI：
10.1038/nphys1932
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发表时间：
2011-06-01
期刊：
影响因子：
19.6
通讯作者：
Shlomo Havlin
中科院分区：
文献类型：
--
作者：
Li Daqing;Kosmas Kosmidis;Shlomo Havlin
系统的维度是表征其结构和基本物理特性的最基本量之一。例如，扩散(1) 和振动激发(2) 以及临界点附近系统的普遍特征都在很大程度上取决于其维度(3,4)。然而，在复杂网络理论中，维度的概念很少被讨论。在此，我们研究了空间嵌入网络模型，并展示了如何确定其维度。我们的研究结果表明，以链接长度的广泛分布为特征的网络，其维度高于嵌入空间的维度。我们用全球航空网络和互联网来说明我们的发现，并认为尽管这些网络嵌入了二维空间，但它们应分别被视为维度接近 3 和 4.5 的系统。我们表明，网络维度不仅是理解网络拓扑结构的关键概念，也是理解网络动态过程（如扩散和包括渗滤在内的临界现象）的关键概念。
The dimension of a system is one of the most fundamental quantities to characterize its structure and basic physical properties. Diffusion(1) and vibrational excitations(2), for example, as well as the universal features of a system near a critical point depend crucially on its dimension(3,4). However, in the theory of complex networks the concept of dimension has been rarely discussed. Here we study models for spatially embedded networks and show how their dimension can be determined. Our results indicate that networks characterized by a broad distribution of link lengths have a dimension higher than that of the embedding space. We illustrate our findings using the global airline network and the Internet and argue that although these networks are embedded in two-dimensional space they should be regarded as systems with dimension close to 3 and 4.5, respectively. We show that the network dimension is a key concept to understand not only network topology, but also dynamical processes on networks, such as diffusion and critical phenomena including percolation.