> Graphs are not only useful as cognitive aides, but are suitable data structures for a wide variety of tasks, particularly on modern parallel processing hardware.
I hope you mean by parallel processing, on a single machine. Reasoning on distributed graphs are difficult to do. The semantic we community could talk for days about what doesn't work.
> Sets: datasets, multisets, posets, alphabets
I guess by alphabets you mean dictionaries.
When you talk about types as graphs I guess you mean nested Objects with collection attributes/types
Where I agree with you is that graphs feel more natural than other structures because our brain is a gigantic graph of neurons.
I don't agree that the web is a directed graph. Not even the semantic web because of a lack of data quality, ridiculous ontologies, and a massive amount of parrtaly duplicating the same instances.
I wouldn't include formula or code parsing because in such cases they are just a means to an end.
What I would include on the other hand are execution plans of data bases which are used for query optimization. You might want to talk here to someone at Oracle.
That all being said, I'd like to reiterate on talking to the semantic web community. Maybe start networking at the ISWC conference first. I always dreamt of every ody's personal knowledge graph where explicit data is linked through everybody's individual ontology into something that is particularly understandable for the creator of the specific ontology.
They definitely need someone with a different perspective. The vuys from Cambridge Semantics are quite good.