Proving the existence of graviton would be the fundamental finding or confirmation needed for modeling gravitation.

The graviton is a hypothetical transportation particle of the gravitation. And if we are thinking that graviton exists that particle would be "just like all other particles". If we are saying that the condition of the existence of graviton is (E>0). That means that the energy minimum for the existence of that particle is like all other materials and particles. 

Energy level must be higher than zero, or the existence of material is ending. But if we are somehow can confirm the existence of graviton, we are facing another interesting question. The existence of gravitational waves is supporting the existence of graviton. And if researchers are somehow or someday finding graviton from the gravitational waves, that thing will be the most fundamental in the world. 

When we are thinking about the existence of gravitons and the form of the gravitational wave is the graviton burst, we are facing one interesting question about the direction of the gravitational waves. Can gravitational wave itself drop in the black hole? 

The finding and proving the existence of graviton can answer the question of what kind of force gravitation is? There is the possibility that gravitation is not an independent force or interaction. But even in that case, the form of gravitation is interesting. The gravitation is the key to the GUT (Grand Unified Theory) which connects all fundamental interactions to the one theory. 

Is it some kind of radiation? And if we are thinking that the gravitation is the part of the same fundamental interactions with the strong nuclear interactions, weak nuclear interaction, and electromagnetism it would be interesting to see how strange nuclear force will turn to gravitation? 

If graviton exists and it's like all other particles in the world that thing causes interesting questions. All other particles have the mirror particle or antiparticle. So there should be the anti-graviton. But how graviton transports gravitation? In some theories, graviton would transport string between objects, and those strings will pull the objects to each other. 

So what that string could be? Could it be the simple radiation ray, which origin is in the gravitons? Are gravitons behave like extremely small black holes, where the radiation comes out from their poles. So are gravitons the origin of some form of mystic dark energy? 

The reason why we cannot see that almost proven particle is probably that particle is a somehow different size than other particles. So the radiation that those particles are sending has a somehow different wavelength than other particles. And that means it cannot interact with sensors, but the gravitation causes the most dominating effect in our world. So gravitation remains a mystery. Why we can feel that force, but we cannot see it? 

()https://en.wikipedia.org/wiki/Fundamental_interaction

()https://en.wikipedia.org/wiki/Grand_Unified_Theory

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