Comments on the Use of Eigenfunctions to Measure Structural Properties of Geographic Networks

Abstract

The use of eigenfunctions has been proposed to measure spatial structure in networks. So far, however, there has been a paucity of applications of the approach, particularly to cellular networks (mosaics). This study uses specially constructed cellular networks which possess very similar degree vectors but dissimilar arrangements of vertex degrees to test the effectiveness of the approach. The results of this test indicate that there are several considerable limitations inherent in the procedure.