Spatial network

thumb|A random geometric graph, one of the simplest models of 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 of spatial network is a 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. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and 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.

Examples

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

Characterizing spatial networks

The following aspects are some of the characteristics to examine a spatial network: Most of the important problems such

as the location of nodes of a network, the evolution of

transportation networks and their interaction with population

and activity density are addressed in these earlier

studies. On the other side, many important points still remain unclear, partly because at that time datasets of large networks and larger computer capabilities were lacking.

Recently, spatial networks have been the subject of studies in Statistics, to connect probabilities and stochastic processes with networks in the real world.

References

Examples

Characterizing spatial networks

See also

References