Eigenfunction properties and approximations of selected incidence matricesemployed in spatial analyses

Mathematical properties of eigenfunctions of selected incidence matrices ap pearing in spatial statistics formulae are summarized. Seven theorems are p roposed and proved, and three conjectures are posited. Results summarized h ere allow the determinant of massively large n x n geographic weights matri ces to be accurately approximated. In addition, the behavior of eigenfuncti ons for graphs affiliated with a linear configuration of connected nodes ar e better understood. (C) 2000 Elsevier Science Inc, All rights reserved.