In the title, the graviton is not a graviton and the liquid is not a (normal) liquid.
[It's not my area, so I may have some errors in my description. Please compare with https://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect ]
The idea is that you vave two semiconductors, and you look at the electrons in the surface between them. If you choose them correctly, the electrons in the surface act very weird. In particular when there is a magnetic field (perpendicular?) to the surface.
The electrons act someone like a liquid. But it's a 2D liquid inside a solid block made of semiconductors, you can't pour it into a glass. I'm not sure why they call it a liquid but in other cases it's common to imagine that the electrons are a gas, so perhaps beeing traped in the correct semiconductors make the more behave as if they were sticky.
Now you consider the exitations of the liquid, imagine that they are like litle swirls that are stable enough to treat them as a fake particle or quasi-particle. (It's like a hurricane in real life that is a lot of clouds, but it's stable enough to get a name. I'm not sure this analogy is 100% accurate, but I hope so.)
In some cases, this small quasi-particles have properties like the graviton.
> Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons.
They are not measuring gravitons, they are measuring something that has some similar properties. It's like a analogic simulation.
The thecnical terms are correct in the reseach area, but outside the research area are very confusing and misleading. (I'm not blaming them, becuse they are publishing it in Nature that is for experts. But I had to remember a few courses, talks and read wikipedia, just to make this explanation that I'm not sure is 100% accurate.)
