The 2MASS redshift survey galaxy group catalogue derived from a graph-theory based friends-of-friends algorithm.

We present the galaxy group catalogue for the recently-completed 2MASS Redshift Survey (2MRS, Macri2019) which consists of 44572 redshifts, including 1041 new measurements for galaxies mostly located within the Zone of Avoidance. The galaxy group catalogue is generated by using a novel, graph-theory based, modified version of the Friends-of-Friends algorithm. Several graph-theory examples are presented throughout this paper, including a new method for identifying substructures within groups. The results and graph-theory methods have been thoroughly interrogated against previous 2MRS group catalogues and a Theoretical Astrophysical Observatory (TAO) mock by making use of cutting-edge visualization techniques including immersive facilities, a digital planetarium, and virtual reality. This has resulted in a stable and robust catalogue with on-sky positions and line-of-sight distances within 0.5 Mpc and 2 Mpc, respectively, and has recovered all major groups and clusters. The final catalogue consists of 3022 groups, resulting in the most complete "whole-sky" galaxy group catalogue to date. We determine the 3D positions of these groups, as well as their luminosity and comoving distances, observed and corrected number of members, richness metric, velocity dispersion, and estimates of $R_{200}$ and $M_{200}$. We present three additional data products, i.e. the 2MRS galaxies found in groups, a catalogue of subgroups, and a catalogue of 687 new group candidates with no counterparts in previous 2MRS-based analyses.