Finding quasar superstructures

We describe a graph theoretical method, using the minimal spanning tree (MST), for finding candidates for quasar superstructures in quasar surveys. The morphology of the candidate can be characterized by the normalized mean, m, and normalized standard deviation, σ, of the edge-lengths of the 2D and 3D MSTs associated with it, This allows comparison with well-known distributions and the determination of the significance of the candidate. We apply this technique to six surveys, three of them with claims of detections of quasar superstructures. These three structures are recovered and in two of the other three surveys we find a new candidate for a superstructure, consisting of ten quasars, at z ~ 1.9, and a grouping of seven Seyfert galaxies at z ~ 0.19. The former grouping has dimensions of ~120 × 90 × 20h–3 Mpc3 and the latter has dimensions of ~60 × 30 × 10h-3 Mpc3.