Representing mobility as a spatial interaction involves several 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.
- Centroid. An abstraction of the attributes of a zone at a point. This is of particular relevance when the attributes generating mobility are zonal (e.g. ZIP codes, cities, states, etc.) while the graphic representation requires specific origins and destinations. For instance, showing flows between ZIP codes would implicitly require the generation of one centroid for each ZIP code.
- Flows. Flows are generally expressed by a valued vector Tij representing an interaction between locations i and j.
- Vectors. On the above figure, two areas, zone i and zone j, are represented as two centroids, i and j. A vector Tij 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.