Thank you for the GraphML. We were able to identify the problem, which is actually a bug in yEd Live's serialization of the pool node.
We have just deployed a fixed version of yEd Live, therefore the pool node should now be written correctly when saved.
That said, these specific GraphMLs can still not be read by yEd Live (or yEd Desktop). We are trying to make it work despite the faulty pool node serialization. However, this needs some more investigation.
For now, you need to correct the files manually by opening them in a text editor and replacing
i.e. deleting the broken attribute. Then, you can open the GraphML in yEd Live as well as in yEd Desktop and you can also save it as usual in both applications.
Afaik, only the "PoolNodeStyle" should be affected but you can also search for '__' (double underscore) which should not appear as an attribute of an XML tag.
Sorry for the inconvenience and thanks again for pointing us to the issue!