Lattice networks (see Fig. 1) are useful models for representing spatial networks. Many physical phenomena have been studied from these structures. Examples include laminate models for spontaneous magnetization,[5]​ diffusion phenomena modeled as random walks[6]​

and filtered.[7]​ To model the resilience of spatially situated interdependent infrastructures, an interdependent lattice network model was recently introduced and analyzed (see Fig. 2)[8]​

.[9]​ A multiple spatial model was introduced by Danziger et al[10]​ and was later analyzed by Vaknin et al.[11]​ See Fig. 3.

In the “real” world many aspects of networks are non-deterministic – randomness plays an important role. For example, new links, representing friendship, are somewhat random on social networks. Modeling spatial networks in relation to stochastic operations makes a lot of sense. In many cases, the Poisson spatial process is used to approximate data sets of processes in spatial networks. Other stochastic aspects of interest are:

Another definition of a spatial network derives from the theory of space syntax. It can be notoriously difficult to decide which spatial element should go in complex spaces that involve large open areas or many interconnected paths. The creators of space syntax, Bill Hillier and Julienne Hanson use the axial line and convex space as spatial elements. Roughly speaking, an axial line is the longest line of sight and access through open space, and a convex space is the polygon. maximum convex" that can be drawn in open space. Each of these elements is defined by the geometry of a local boundary in different regions of the space map. The decomposition of the space map into a complete set of intersecting axial lines or overlapping convex spaces produces the axial map or overlapping convex map. Algorithmic definitions of these maps exist, allowing mapping from an arbitrarily modeled space to a network arranged in mathematical graphs so that it can be realized in terms relatively well-defined maps. Axial maps are used to analyze urban networks"), in which the system generally comprises linear segments, while convex maps are more often used to analyze building plans where spatial patterns are often articulated in a convex manner, although both axial and convex maps can be used in either case.

Currently, there is a fraction within the space syntax community seeking to better integrate with geographic information systems (GIS), and much of the software produces interlinks with commercially available GIS systems.

While networks and graphs have long been the subject of many studies in mathematics, physics, mathematical sociology,

computer science, spatial networks were intensively studied during the 1970s by quantitative geography. Objects of study in geography are, among others, the locations, activities and flows of individuals, but also networks involving time and space.[12] Most of the important problems, such as the location of nodes in a network, the evolution of transport networks and their interaction with population and activity density are addressed in these early studies. On the other hand, many important points remain unclear, in part because large network data sets and sufficient computer capabilities did not exist.

Recently, spatial networks have been the subject of studies in Statistics, to connect probabilities and stochastic processes with real-world networks.[13]​.

Lattice networks (see Fig. 1) are useful models for representing spatial networks. Many physical phenomena have been studied from these structures. Examples include laminate models for spontaneous magnetization,[5]​ diffusion phenomena modeled as random walks[6]​

and filtered.[7]​ To model the resilience of spatially situated interdependent infrastructures, an interdependent lattice network model was recently introduced and analyzed (see Fig. 2)[8]​

.[9]​ A multiple spatial model was introduced by Danziger et al[10]​ and was later analyzed by Vaknin et al.[11]​ See Fig. 3.

In the “real” world many aspects of networks are non-deterministic – randomness plays an important role. For example, new links, representing friendship, are somewhat random on social networks. Modeling spatial networks in relation to stochastic operations makes a lot of sense. In many cases, the Poisson spatial process is used to approximate data sets of processes in spatial networks. Other stochastic aspects of interest are:

Another definition of a spatial network derives from the theory of space syntax. It can be notoriously difficult to decide which spatial element should go in complex spaces that involve large open areas or many interconnected paths. The creators of space syntax, Bill Hillier and Julienne Hanson use the axial line and convex space as spatial elements. Roughly speaking, an axial line is the longest line of sight and access through open space, and a convex space is the polygon. maximum convex" that can be drawn in open space. Each of these elements is defined by the geometry of a local boundary in different regions of the space map. The decomposition of the space map into a complete set of intersecting axial lines or overlapping convex spaces produces the axial map or overlapping convex map. Algorithmic definitions of these maps exist, allowing mapping from an arbitrarily modeled space to a network arranged in mathematical graphs so that it can be realized in terms relatively well-defined maps. Axial maps are used to analyze urban networks"), in which the system generally comprises linear segments, while convex maps are more often used to analyze building plans where spatial patterns are often articulated in a convex manner, although both axial and convex maps can be used in either case.

Currently, there is a fraction within the space syntax community seeking to better integrate with geographic information systems (GIS), and much of the software produces interlinks with commercially available GIS systems.

While networks and graphs have long been the subject of many studies in mathematics, physics, mathematical sociology,

computer science, spatial networks were intensively studied during the 1970s by quantitative geography. Objects of study in geography are, among others, the locations, activities and flows of individuals, but also networks involving time and space.[12] Most of the important problems, such as the location of nodes in a network, the evolution of transport networks and their interaction with population and activity density are addressed in these early studies. On the other hand, many important points remain unclear, in part because large network data sets and sufficient computer capabilities did not exist.

Recently, spatial networks have been the subject of studies in Statistics, to connect probabilities and stochastic processes with real-world networks.[13]​.