Hi Arnold,
That's a great question. I'm guessing that you are using the Generate Spatial Weights Matrix tool, which would explain why you aren't seeing the Polygon Contiguity (First Order) option in the drop-down. In the Generate Spatial Weights Matrix tool, there are actually two options for polygon contiguity...Contiguity_Edges_Only and Contiguity_Edges_Corners. The Contiguity_Edges_Only option is the exact same conceptualization as Polygon Contiguity (First Order)...they both use edges only to determine if features are neighbors, while the Contiguity_Edges_Corners option uses either edges OR corners. A good way to think about this is by visualizing a chess board. The Contiguity_Edges_Only and Polygon Contiguity (First Order) options consider features neighbors ONLY if they are directly next to each other (ie they share edges). The Contiguity_Edges_Corners option considers features neighbors if they are next to each other, and also if they are diagonal to each other with a corner touching. See attached image.
So, there are several tools in the Spatial Statistics toolbox that refer to the edges-only option as Polygon Contiguity (first order)...including hot spot analysis, spatial autocorrelation, cluster and outlier analysis, and high/low clustering. The Generate Spatial Weights Matrix tool, however, calls this option CONTIGUITY_EDGES_ONLY because there are two options and those names are more descriptive.
Hope this helps!
Lauren Rosenshein
Geoprocessing Product Engineer
