As Chris stated, it's certainly not trivial on database level, but if you're looking for a solution on application level, you might have a look at Structr, a framework on top of and tightly integrated with Neo4j.
It provides node-level security based on ACLs, with users, groups, and different access levels. The security in Structr is implemented on the lowest level possible, f.e. we only instantiate objects if the querying user has the approriate access rights.
All higher access levels like REST API and UI see only the records available in the user's context.