Representation of a Movement as a Spatial Interaction

Movements can be simplified in three basic categories: freight, people and information. Representing a movement as a spatial interaction involves the following considerations:

Locations. A movement is occurring between a location of origin and a location of destination. i generally denotes an origin while j is a destination. The representation of origins and destinations commonly involves centroids. A centroid is an abstraction of a the attributes of a zone at a point. This is of particular relevance when the attributes of the movements considered are zonal (e.g. ZIP codes, cities, states, etc.) while the graphic representation of these movements requires specific origins and destinations. For instance, showing flows between ZIP codes on a GIS would implicitly require the generation of one centroid for each ZIP code.
Flows. Flows are generally expressed by a valued vector T_ij, representing an interaction between locations i and j.

On the above figure, two geographic zones, zone i and zone j, are expressed by two centroids, i and j. A vector T_ij links two centroids and has a value assigned to it (50) which can represents movements such as tons of freight, numbers of passengers per day, or number of phone calls.