If gravitons are 'real' and analogous to photons are they also being 'stretched' by the universe's expansion? Since photon wavelengths are stretched by our expanding universe, appearing to us as a redshift, would graviton wavelengths similarly be stretched?  For that matter, do gravitons even have a wavelength like photons?
 A: What has just been proven is the existence of gravitational waves, not gravitons. Beside, if graviton exists, they are likely  to be a "pseudo particle" like the photon, i.e., mostly a quantized emission of wave packet.
As a wave, by construction the downstream part is late compared to the upstream part, and because of expansion, it will have slightly more length to cross than the uptream part at anytime, which accumulates with distance, resulting into the increase of the wavelenght. All kinds of waves thus "red"shift.
A: Suppose, there are gravitons, and space is expanding.
Gravitons stretching with stretching space, would loose strength in same way as lower frequency (red shifted) light has lesser energy. That would change laws of gravity constantly. At the least, it would keep changing gravitational constant. That does not seem to be the case. There are no colors in gravity.
Gravity appears to be apart from all other stuff. It is property of space that becomes evident in presence of mass/energy. The space has this property everywhere but it becomes intense (curved inward) due to presence of mass/energy. It seems to be a property, and not any particle. Most fundamental property (gravity) of most fundamental entity (empty space).
We keep going smaller and smaller, the particles must end at some level and we will have to deal with emptiness in any case. It is just a matter of - at what level. 
