We basically follow the method of Yang et al. 2007. We start with the best-fitting central galaxy stellar-halo mass relation in Guo et al. (2018), assign the halo mass for each galaxy, and find groups. As the BOSS galaxies are incomplete due to the complicated target selections, we then iterate by assigning new halo mass to each group using the completeness functions in Guo et al. (2018) with the abundance matching method until it converges.

We note that there is a completeness value for each group, determined by the stellar mass completeness of its central galaxy, meaning the fraction of observed central galaxies in a given stellar mass bin. For group completeness below 0.1, we simply assign the halo mass using the central galaxy stellar-halo mass relation, which is not as accurate for such low completeness groups. So we recommend to use groups with completeness above 0.1, or better with completeness > 0.5. 

We assumed the Planck cosmology of Omega_m=0.307, h=0.678, sigma_8=0.823. The redshift range of the group catalog is limited to 0.1<z<0.8 for the BOSS sample. The information of the two files is as follows:

BOSS_galaxy.dat:

1. ra 2. dec 3. z
4. is satellite? (0 for central, 1 for satellite)
5. stellar mass (M_sun)
6. group total stellar mass (M_sun)
7. halo mass (M_sun)
8. halo virial radius (Mpc/h)
9. stellar mass completeness of its group central (fraction of observed central galaxies in a given stellar mass bin), for groups with completeness lower than 0.1, the halo mass is estimated from the central galaxy SHMR
10. group id 
11. number of group members

BOSS_group.dat:

1. group id
2. RA 3. dec 4. z (RA, DEC, z of the groups are mass-weighted average of the members)  
5. stellar mass of the central galaxy (defined as the most massive member) (M_sun)
6. group total stellar mass (M_sun) 
7. halo mass (M_sun)
8. halo virial radius (Mpc/h)
9. group completeness 
10. number of group members