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spatial network
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are ''spatial elements'' associated with geometric objects, i.e. the nodes are located in a space equipped with a certain metric.〔M. Barthelemy, "Spatial Networks", Physics Reports 499:1-101 (2011) ( http://arxiv.org/abs/1010.0302 ).〕 The mathematical simplest realization is a Random geometric graph where nodes are distributed uniformly at random onto two-dimensional plane and connected if the Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, 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 and the evolution of spatial networks is crucial for many different fields ranging from urbanism to epidemiology.
== Examples ==
An urban spatial network can be constructed by abstracting intersections as nodes and streets as links, which is referred to as transportation network analysis. One might think of the 'space map' as being the negative image of the standard map, with the open space cut out of the background buildings or walls.〔Hillier B, Hanson J, 1984, The social logic of space (Cambridge University Press, Cambridge, UK).〕
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