Polygon networks are usually described qualitatively as becoming more regular through time, but such a concept has yet to be demonstrated numerically. The aim of this study is to address this question quantitatively in order to determine if polygonal terrain networks actually become more regular as they develop. Spatial point pattern analysis (SPPA), which can quantify overall network geometries based on the randomness or regularity exhibited by the spatial arrangement of polygon-bounding trough intersections, was used at three ice-wedge polygon sites in the Canadian High Arctic. SPPA was applied in two ways: (i) on the present-day networks observed in the field; and (ii) on historical arrangements derived by distinguishing primary from secondary troughs. In all cases, the polygonal networks had undergone a statistically significant regularisation over the course of their development. Although the method was applied only to terrestrial ice-wedge polygons, such an approach may also be useful for interpreting the evolution of Antarctic sublimation polygons and geometrically similar polygonal networks on Mars. Copyright © 2012 John Wiley & Sons, Ltd. and Her Majesty the Queen in Right of Canada.