In our paper Karachentseva, Karachentsev & Melnyk (2011) we found that 125 2MIGs from the total number 3227 have 214 faint neighbours with radial velocity differences of dV < 500 km/s and projected separations of Rp < 500 kpc relative to the 2MIG galaxies. These neighbours are much fainter (smaller) than isolated galaxies that is why they did not meet the isolation criteria.
The median luminosity of the companions is 1/25 of the luminosity of catalog galaxies, which has little effect on the dynamic isolation of the latter. The median ratio of the orbital mass to the K-luminosity determined from 60 companions of E and S0 2MIG galaxies, 63 M⊙/L⊙, is signficantly greater than that found from the spiral galaxy companions (17 M⊙/L⊙). We note that a fraction of 2MIG galaxies with companions may be a part of low-contrast diffuse structures: clouds and filaments.
Moreover, in our paper Melnyk, Mitronova & Karachentseva (2013) we compared luminosities and g-r colours of 2MIG galaxies which have faint companions and which do not have them. We fount that isolated galaxies with faint companions are in general more massive than those without any neighbours. It was laso shown that E-type galaxies with and without companions have completely same colours. Meanwhile spiral galaxies of 2MIGs with small companions are slightly redder that isolated galaxies without any neighbours.
Therefore we see that an environmental influence is very important factor of galaxy evolution which is observed even by the impact of the small faint neighbours.