Spatial Network

http://en.wikipedia.org/wiki/Spatial_network

A spatial network is a network of spatial elements. In physical space (which typically

includes urban or building space) spatial networks are derived from maps of open space

within the urban context or building. 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 space map is then broken into units; most simply, these might be

road segments. The road segments (the nodes of the graph) can be linked into a network via

their intersections (the edges of a graph). A common instance of a spatial network , the

transportation network analysis, reverses this and treats the road segments as edges and the

street intersections as nodes in the graph. More generally, the term 'spatial network' has

come to be used to describe any network in which the links (or potential links) between

nodes are constrained by the location of the nodes in some kind of 'space'. In this situation the

topology of the network can be considered exogenous to the model. This more general notion

of spatial network is currently receiving considerable interest from those looking at scale

free networks, complex networks and small world networks. A particularly advanced form

of spatial network derives from the theory of space syntax. It can be notoriously difficult to

decide what a spatial element should be in complex spaces involving large open areas or

many interconnected paths. The originators of space syntax, Bill Hillier and Julienne

Hanson use axial lines and convex spaces as the spatial elements. Loosely, an axial line is the

'longest line of sight and access' through open space, and a convex space the 'maximal

convex polygon' that can be drawn in open space. Each of these elements is defined by the

geometry of the local boundary in different regions of the space map. Decomposition of a

space map into a complete set of intersecting axial lines or overlapping convex spaces

produces the axial map or overlapping convex map respectively. Algorithmic definitions of

these maps exist, and this allows the mapping from an arbitrary shaped space map to a

network amenable to graph mathematics to be carried out in a relatively well defined

manner. Axial maps are used to analyse urban networks, where the system generally

comprises linear segments, whereas convex maps are more often used to analyse building

plans where space patterns are often more convexly articulated, however both convex and

axial maps may be used in either situation. Currently, there is a move within the space

syntax community to integrate better with geographic information systems (GIS), and

much of the software they produce interlinks with commercially available GIS systems.