In the framework of Dark Matter by Quantum Gravitation (DMbQG) theory, the Direct mass gives the total mass into the halo region, growing with the square root of radius. This formula has only one parameter specific for each galaxy.The NFW profile is a universal method that gives the DM mass function depending on radius at the disk and galactic halos. This function is defined by two parameters. The DMbQG claims that DM is generated by the own gravitational field and consequently the DM halo is unbounded. In the paper [1] Abarca,M. was proved that it is the Dark energy the mechanism able to counterbalance the DM.As the direct mass is linked to the total mass (baryonic plus DM), in the paper has been developed a method to integrate the baryonic matter into the NFW DM function in order to be able to compare both functions connected to the total mass. Thanks this method has been possible to define the R200-TOTAL and the M200-TOTAL both referred to a sphere whose total mass has a mean density equal to 200 times the critic density of the Universe.The main achievement of this paper is to demonstrate that the Direct mass function and the NFW-total mass function are equivalents into the halo region of MW and the M31. The equivalence of the two formulas for masses is based on four tests, all of them tested successfully. Test I. Comparison the R(200-TOTAL) and the M(200-TOTAL) calculated by the two different formulas, for MW and M31. Test II. Using the M(200-TOTAL), value that is given by the NFW method, is calculated the parameter a^2 which is compared with the one got in the framework of DMbQG theory. Test III. Is similar to test III but using the R200-TOTAL and the M200-TOTAL and the result is successful as well.Test IV. The direct mass function and the NFW-total mass function are compared into the halo region up to R(200-TOTAL). Although the thesis of this paper is for any galaxies, the calculus has been made with MW and M31, because they are the best well studied galaxies and his data have the maximum of accuracy. The prove reach in this paper is valuable because the Direct mass which comes from DMbQG theory gives similar results to the NFW function mass, which is a trustable profile for DM, tested in thousand of galaxies,.