Minimal spanning trees, filaments and galaxy clustering

Abstract

We describe a graph theoretical technique for assessing intrinsic patterns in point data sets. A unique construction, the minimal spanning tree, can be associated with any point data set given all the inter-point separations. This construction enables the skeletal pattern of galaxy clustering to be singled out in quantitative fashion and differs from other statistics applied to these data sets. We describe and apply this technique to two- and three-dimensional distributions of galaxies and also to comparable random samples and numerical simulations. The observed CfA and Zwicky data exhibit characteristic distributions of edge-lengths in their minimal spanning trees which are distinct from those found in random samples. These statistics are also re-evaluated after normalizing to account for the level of clustering in the samples.