MODELS FOR SPATIAL WEIGHTS: A SYSTEMATIC LOOK

General properties of spatial weights models, in particular Markovian properties, are systema- tically investigated. The role of stationary spatial distribution, interpretable as an importance-centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the asso- ciated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry and Dirichlet-Voronoi tessellations illustrate the main concepts, with a particular geometri- cal emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered form general models.

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