Filaments are one of the most prominent features visible in the galaxy distribution. Considering the luminous red galaxies in the Sloan Digital Sky Survey Data Release Seven (SDSS DR7), we have analysed the filamentarity in 11 nearly 2D sections through a volume limited subsample of these data. The galaxy distribution, we find, has excess filamentarity in comparison to a random distribution of points. We use a statistical technique ‘Shuffle’ to determine LMAX, the largest length-scale at which we have statistically significant filaments. We find that LMAX varies in the range 100–130 h−1 Mpc across the 11 slices, with a mean value LMAX= 110 ± 12 h−1 Mpc. Longer filaments, though possibly present in our data, are not statistically significant and are the outcome of chance alignments.