A great deal of attention has recently been paid to determining sub-communities on the basis of relations, corresponding to edges, between individuals, corresponding to vertices out of an unlabelled graph (Neman, SIAM Review 2003; Airoldi et al JMLR 2008; Leskovec & Kleinberg et al SIGKDD 2005) for probabilistic ergodic models of infinite unlabelled graphs. We drive consistency properties of the Newman-Girvon index, and develop an index with better consistency properties and better performance on simulated data sets. This is joint work with Aiyou Chen.