We use a volume-limited sample of quasars in the Sloan Digital Sky Survey (SDSS) DR7 quasar catalog to identify quasar groups and address their statistical significance. This quasar sample has a uniform selection function on the sky and nearly a maximum possible contiguous volume that can be drawn from the DR7 catalog. Quasar groups are identified by using the Friend-of-Friend algorithm with a set of fixed comoving linking lengths. We find that the richness distribution of the richest 100 quasar groups or the size distribution of the largest 100 groups are statistically equivalent with those of randomly-distributed points with the same number density and sky coverage when groups are identified with the linking length of 70 h−1Mpc. It is shown that the large-scale structures like the huge Large Quasar Group (U1.27) reported by Clowes et al. (2013) can be found with high probability even if quasars have no physical clustering, and does not challenge the initially homogeneous cosmological models. Our results are statistically more reliable than those of Nadathur (2013), where the test was made only for the largest quasar group. It is shown that the linking length should be smaller than 50 h−1Mpc in order for the quasar groups identified in the DR7 catalog not to be dominated by associations of quasars grouped by chance. We present 20 richest quasar groups identified with the linking length of 70 h−1Mpc for further analyses.

Abstract
1. INTRODUCTION
2. SDSS QUASAR CATALOG
3. IDENTIFICATION OF QUASAR GROUPS
4. COMPARISON WITH RANDOM DISTRIBUTIONS
5. SUMMARY AND CONCLUSIONS
REFERENCES

• Changbom Park(School of Physics, Korea Institute for Advanced Study)
• Hyunmi Song(School of Physics, Korea Institute for Advanced Study) Corresponding author
• Maret Einasto(Tartu Observatory)
• Heidi Lietzen(Instituto de Astrof´ısica de Canarias/Universidad de La Laguna, Dept. Astrof´ısica)
• Pekka Hein¨am¨aki(Tuorla Observatory, University of Turku)