Einstein’s theory of gravity is very good at explaining the behavior of large objects. General relativity also gives us some insight into the nature of gravitons. In general relativity, the distribution of mass and energy in the universe is described by a four-by-four matrix that mathematicians call a tensor of rank two. This is important because if the tensor is the source of gravitation, you can show that the graviton must be a particle with a quantum mechanical spin of two. Another nice fallout of this correspondence is that the graviton is the only possible massless, spin two particle. If you observe a massless, spin two particle, you have found the graviton.

http://www.pbs.org/wgbh/nova/blogs/physics/2014/05/what-are-gravitons/

In gravitational blueshif, gravitons behave like electromagnetic fields and cause increased photon's energy (in fact, intensity of electromagnetic fields). So, we need a new definition of graviton.

https://www.researchgate.net/publication/268343642_A_new_Definition_of_Graviton?ev=prf_pub

Article A new Definition of Graviton

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