SQL is an implementation of relational algebra, and databases that implement it are relational databases for storing relational data.
Pointing at the name of a thing isn't an argument, I admit it, but asking "what could go wrong if we want to use a system tailored to relational data to deal with non-relational data?" strikes me as the sort of question that might turn out to have a compelling answer 6 months in when it is too late to easily change the database.
If I were involved in a project, I would be representing very hard that the data comes out of the relational DB using "SELECT * FROM table WHERE conditions" and then the clever graph things start happening. If the data needs to be read from disk using clever graph based algorithms, then use a clever, graph-based database. There are a bunch out there according to Wikipedia.