I have created a mask in the UV editor and I've animated the movement of the edges of the mask with keyframes in the dope sheet. However if I switch to the graph editor I can't find my mask with the keyframe values of the position of the edges of the mask. How do I find these values?
I am not 100% sure, what you mean by "created a mask in the UV editor", because as far as I know the only way to make masks in Blender is in either the image or the movie clip editor. But maybe I am missing something.
If you mean that you want to animate an edge of the unwrap of an object, then the short answer is that Blender cant do that. A really quick google search unearthed this addon, though: https://www.blendernation.com/2011/11/12/animating-uv-textures/
If you are already using it and are wondering why these properties still dont show up in the graph editor, you should probably try to contact the developer directly.