A 2D analysis of percolation and filamentarity in the SDSS DR1
  We have used the Largest Cluster Statistics and the Average Filamentarity to quantify respectively the connectivity and the shapes of the patterns seen in the galaxy distribution in two volume limited subsamples extracted from the equatorial strips of the Sloan Digital Sky Survey (SDSS) Data Release One (DR1). The data was projected onto the equatorial plane and analyzed in two dimensions (2D). Comparing the results with Poisson point distributions at various levels of smoothing we find evidence for a network like topology with filaments being the dominant patterns in the galaxy distribution. With increasing smoothing, a transition from many individual filamentary structures to an interconnected network is found to occur at a filling factor 0.5-0.6. We have tested the possibility that the connectivity and the morphology of the patterns in the galaxy distribution may be luminosity dependent and find significant evidence for a luminosity-morphology relation, the brighter galaxies exhibiting lowers levels of connectivity and filamentarity compared to the fainter ones. Using a statistical technique, Shuffle, we show that the filamentarity in both the SDSS strips is statistically significant up to 80 Mpc/h but not beyond. Larger filaments, though identified, are not statistically significant. Our findings reaffirm earlier work establishing the filaments to be the largest known statistically significant coherent structures in the universe. 
Biswajit Pandey and Somnath Bharadwaj (IIT Kharagpur, India)