Spatial network

[1][2] 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.

Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for many different fields ranging from urbanism to epidemiology.

Indeed, the airline passenger networks is a non-planar example: Many large airports in the world are connected through direct flights.

Other stochastic aspects of interest are: Another definition 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.

Objects of studies in geography are inter alia locations, activities and flows of individuals, but also networks evolving in time and space.

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.