Andy Long
For the SA game, described in [2], we've used the Rook's definition of contiguity: that is, we consider two cells of a matrix to be neighbors if they share a common boundary. Alternatively, we might have chosen the Bishop definition (neighbors if two cells share a corner), or the Queen's definition (neighbors if neighbors by either the Rook's or Bishop's definitions). These names relate to chess, of course, and the moves that each of the three pieces are allowed to make. No one, to my knowledge, has proposed the Knight's definition!
Start with a matrix of data values 
. Let W be the weight
matrix, such that 
if and 
are neighbors (using the Rook's
definition), and 0 otherwise; and let 
(basically a mean-centered 
vector). Then we calculate the following
statistics[1]: