I've been thinking about graph databases recently. Some points:
- Cypher is an interesting query language (as an alternative to SQL) because it does not force the concept of tables into a user's mental model. Tables are ultimately an arbitrary construct that were originally introduced as a mathematical construct for helping formalize "the relational model". They were not conceived with UX in mind and it shouldn't be too controversial to conclude that they add a lot of day-to-day complexity to SQL (normalization, key constraints, indices...).
- Neo4j's data storage tech is not interesting, since its big idea is simply to store all data as pointer spaghetti. Other than that, it uses indices just like SQL DBs. Also on this point: if you're just trying to find a good programming model for users, then the underlying implementation details of your system are interchangeable and thus irrelevant.