Why can't there be cycles in the Merkle graph

That would be cool. You just have a partial order between children and parents, like in git.

This is a good paper that covers hashing graphs (including ones with cycles): "On Hashing Graphs" https://eprint.iacr.org/2012/352.pdf

Wow, very interesting.

Can you summarizd how the actual algorithm is supposed to work, ie its main ideas?

I am surprised to find that using sha hashes in a tree or DAG will leak information to people who shouldn't have it. Is this a serious flaw and how do these guys ultimately solve the problem? I read the paper but the algorithm seems a bit hard to understand and follow.

Consider the simplest cycle, a node that points to itself. To create it, you must include the content hash of the document in the document itself.

To do that, you need to generate a collision. You enter a random content hash in the document, then keep modifying the document and hashing it untill it's hash matches the one you included. It's not impossible, but depending on the hash function, it may take you a very long while to find it.

You would need to know the hash of a yet-to-exist node to create cycles on a Merkle graph :)

It is really not that different than the 'Grandfather Parsdox': Merkel graphs are inherently 'causal sequences' and when combined with nodes as 'spaces of things' they define the evolving manifold of a 'world of things'. This seems to inform a sort of deep structure in our reality manifesting in phenomena such as Golden Section, etc. [speculaing at the end there, of course.]