Ring statistics in a 2D graph can be tracked easily, as the excluded volume of the beads in the polymer model means that the polymers naturally form a planar graph with a defined embedding in a periodic plane under all but the most extreme conditions. The rings are then found as being nodes in the dual graph of the polymer graph; the dual graph can be found either by computing an anticlockwise ordering of edges around each node (de Berg ( )), or by computing the Delaunay triangulation of the points and re-joining the triangulation into rings ). In this work we use the latter method as we often wish to compute the Delaunay triangulation anyway for analysing networks ), and it can be simpler to treat algorithmically for a periodic simulation cell.