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We test the Friends-of-Friends (FoF) grouping algorithm, which depends on twolinking lengths (LLs), plane-of-sky and line-of-sight (LOS), normalized to themean nearest neighbor separation of field galaxies. We argue, on theoreticalgrounds, that LLs should be $b_\perp \simeq 0.11$, and $b_\parallel \simeq 1.3$to recover 95% of all galaxies with projected radii within the virial radius$r_{200}$ and 95% of the galaxies along the LOS. We then predict that 80 to 90%of the galaxies in FoF groups should lie within their parent real-space groups(RSGs), defined within their virial spheres. We test the FoF extraction for16x16 pairs of LLs, using subsamples of galaxies, doubly complete in distanceand luminosity, of a flux-limited mock SDSS galaxy catalog. We find thatmassive RSGs are more prone to fragmentation, while the fragments typicallyhave low estimated mass, with typically 30% of groups of low and intermediateestimated mass being fragments. Group merging rises drastically with estimatedmass. For groups of 3 or more galaxies, galaxy completeness and reliability areboth typically better than 80% (after discarding the fragments). Estimatedmasses of extracted groups are biased low, by up to a factor 4 at low richness,while the inefficiency of mass estimation improves from 0.85 dex to 0.2 dexwhen moving from low to high multiplicity groups. The optimal LLs depend on thescientific goal for the group catalog. We propose $b_\perp \simeq 0.07$, with$b_\parallel \simeq 1.1$ for studies of environmental effects, $b_\parallel\simeq 2.5$ for cosmographic studies and $b_\parallel \simeq 5$ for followupsof individual groups.

How well does the Friends-of-Friends algorithm recover group properties from galaxy catalogs limited in both distance and luminosity?