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此词条由城市科学读书会词条梳理志愿者（Yukiweng）翻译审校，未经专家审核，带来阅读不便，请见谅。

此词条由城市科学读书会词条梳理志愿者（Yukiweng）翻译审校，未经专家审核，带来阅读不便，请见谅。

[[文件:Random geometric graph.svg|链接=link=Special:FilePath/Random_geometric_graph.svg|缩略图|201x201像素|随机几何图，最简单的空间网络模型之一。]]

[[文件:Random geometric graph.svg|链接=link=link=Special:FilePath/Random_geometric_graph.svg|替代=|缩略图|随机几何图，最简单的空间网络模型之一。]]

A '''spatial network''' (sometimes also '''[[Geometric graph theory|geometric graph]]''') is a [[Graph (discrete mathematics)|graph]] in which the [[Vertex (graph theory)|vertices]] or [[Edge (graph theory)|edges]] are ''spatial elements'' associated with [[Geometry|geometric]] objects, i.e., the nodes are located in a space equipped with a certain [[Metric (mathematics)|metric]].<ref name="Bart">{{cite journal | last1 = Barthelemy | first1 = M. | year = 2011| title = Spatial Networks | arxiv = 1010.0302 | journal = Physics Reports | volume = 499 | issue = 1–3 | pages = 1–101 | doi=10.1016/j.physrep.2010.11.002 | bibcode = 2011PhR...499....1B| s2cid = 4627021 }}</ref><ref name="Bart2">M. Barthelemy, "Morphogenesis of Spatial Networks", Springer (2018).</ref> The simplest mathematical realization of spatial network is a [[Lattice graph|lattice]] or a [[random geometric graph]] (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the [[Euclidean distance]] is smaller than a given neighborhood radius. [[Transport network|Transportation and mobility networks]], [[Internet]], [[cellular network|mobile phone networks]], [[electrical grid|power grids]], [[social network|social and contact networks]] and [[neural network|biological neural networks]] are all examples where the underlying space is relevant and where the graph's [[topology]] alone does not contain all the information. Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for many different fields ranging from urbanism to epidemiology.

A '''spatial network''' (sometimes also '''[[Geometric graph theory|geometric graph]]''') is a [[Graph (discrete mathematics)|graph]] in which the [[Vertex (graph theory)|vertices]] or [[Edge (graph theory)|edges]] are ''spatial elements'' associated with [[Geometry|geometric]] objects, i.e., the nodes are located in a space equipped with a certain [[Metric (mathematics)|metric]].<ref name="Bart">{{cite journal | last1 = Barthelemy | first1 = M. | year = 2011| title = Spatial Networks | arxiv = 1010.0302 | journal = Physics Reports | volume = 499 | issue = 1–3 | pages = 1–101 | doi=10.1016/j.physrep.2010.11.002 | bibcode = 2011PhR...499....1B| s2cid = 4627021 }}</ref><ref name="Bart2">M. Barthelemy, "Morphogenesis of Spatial Networks", Springer (2018).</ref> The simplest mathematical realization of spatial network is a [[Lattice graph|lattice]] or a [[random geometric graph]] (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the [[Euclidean distance]] is smaller than a given neighborhood radius. [[Transport network|Transportation and mobility networks]], [[Internet]], [[cellular network|mobile phone networks]], [[electrical grid|power grids]], [[social network|social and contact networks]] and [[neural network|biological neural networks]] are all examples where the underlying space is relevant and where the graph's [[topology]] alone does not contain all the information. Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for many different fields ranging from urbanism to epidemiology.