The energy of a graviton has to be hf

https://en.wikipedia.org/wiki/Graviton

Wikipedia states: "it is unclear which variables might determine graviton energy."

Let us assume that we have a mass M attached to a harmonic oscillator whose frequency is f. The harmonic oscillator device A is attached to the crust of Earth.

When the mass M swings in the oscillator, it produces a dipole gravitational wave.

Earth, in turn, produces an opposite dipole wave, which - far away - almost exactly cancels the dipole wave produced by M. This is the reason why observed gravitational waves are quadrupole, not dipole.

Let us then assume that we have another harmonic oscillator B of the frequency f close to our first oscillator A.

According to quantum mechanics, the oscillator A can only lose energy in units of hf, where h is the Planck constant.

If the gravitational interaction can transfer energy from A to B, it must happen in units hf. This strongly suggests that the energy of a single graviton is hf, just as it is for a single photon.

But does the oscillator A lose energy at all? Could it be that any energy state of A is stable under the gravitational interaction and cannot decay into a lower energy state?

If the mass M is huge, then we believe that gravitation behaves in a classical way. The oscillator B will certainly start to oscillate if A oscillates. This behavior might be measurable using a Cavendish torsion balance.

https://en.wikipedia.org/wiki/Cavendish_experiment

Thus, there is every reason to believe that the oscillator A can transfer energy packets of the size hf to B.

Conclusions

The energy of a graviton is most probably hf. It is the same energy as for a photon of the same frequency. The "reason" for the packet size is that a quantum harmonic oscillator can only gain or lose energy in packets of the size hf.