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. The simplest mathematical realization is a lattice or a random geometric graph, 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. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and 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.

An urban spatial network can be constructed by abstracting intersections as nodes and streets as links, which is referred to as, resilience transportation network. 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.

The following aspects are some of the characteristics to examine a spatial network:

In many applications, such as rail, roads, and other transportation networks the network is assumed to be planar. Planar networks build up an important group out of the spatial networks, but not all spatial networks are planar. Indeed, the airline passenger networks is a non-planar example: All airports in the world are connected through direct flights.

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