  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.
